Thanks to this forum and some sanity that my SO possesses on occasion, we did not move in together, but he rather bought a house within minutes from me. It's a win-win. I already have my sanctuary to retreat to and he has a (temporary) escape when things get really nuts. 
 

When I stepped in, kids got diagnosed and medicated, some further assessments are still in process, but things don't look too good: they already have ADHD, and it appears the 10y.o. will also be diagnosed with ASD. We're also suspecting either ODD or CD for the elder one (14), which are a standard combination in jail population. 

The younger one shows affection and empathy when in good place, but that's hit and miss. His constant sound making, squealing and screeching when he doesn't get his way normally evoke white-hot rage in me. Like you, I grew up in very austere circumstances, also in an objectively unsafe country, so watching this performance when he gets the "wrong" synthetic cheese on his bathroom-sponge like bread made to order by dad or the wrong amount of sauce does not make me like him more. Unlike you, I can leave when things start hitting the fan. I can't not imagine what it'd be like to be trapped with these creatures for the next decade or so. 
 

I am now much calmer, but that's because I started practicing some radical disengagement: when they refuse to go to school or to take their meds, or when they insist on eating only garbage bagged food from the freezer section, I actively remind myself "not my problem". That has become my mantra. 
I have also made decisions about being seen together in public, going on holidays or even weekends away together: this is no longer happening and I'm happier for it. I don't know if you can afford this type of changes, but I'd think it would be more relaxing for you and your babies to stay at home and plan multiple local activities while your DH takes the demon spawn with him for some bonding opportunities, than you risking your sanity by being stuck with him in a holiday place. I personally find my SO's kids' behaviour shameful- they are destructive and act like complete ferals in nice restaurants, other people's homes, museums etc. I would not dream taking them to a theatre, as they'd have no issues acting like halfwits making stupid noises during the show and laughing about it, completely unperturbed by how idiotic they appear. 
 

It is sad though, because this disengagement seems to have coincided with evaporation of any positive feelings towards them from me. Of course, on occasion I get glimpses of their vulnerable, kind and thoughtful sides, and I know they're just kids, and I hope that these are the facets of their personality they'll eventually grow into, but as the same time they're too few and far between for me to care. 
 

And lastly, I have now begrudgingly agreed (at being almost middle-aged) that nature often wins over nurture. For decades I was wide-eyed "all you need is love" kind of person, albeit not completely naive and dazed, but I clearly see the BM's family in these kids. The BM is deceased, and she had no issues making them on her death bed, while lying about the reality of her condition. Every SINGLE person in her immediate family (parents, siblings, her) had a significant physical or mental health issue (all needing ongoing care and of course all were on welfare outside some occasional menial jobs). The grandfather has some interesting history and is a creep, while grandma is a sweet enabler. I've figured out straight away his family name was made up and doesn't exist outside this particular family (am familiar with their ethnicity), and also supposedly he sought refuge for political reasons, but I'm wondering what he really got up to and whether the justice system there was on his a$$ for other matters. Pity I have no way of finding out without his actual family name. 
 

Anyway, wishing you strength and commiserating, and most of all wishing you disengagement opportunities. 

All THREE of Chef's ferals, culminating in YSS literally crapping all over my house on purpose because he didn't get his way.  This was at the same age as your SS.  Even then Chef didn't want to do anything about it.  The attention seeking was monumental by all three.  

The BM called CPS on us because Chef dared to put SD in time out for kicking YSS.  Then she got all three skids to lie and say we were "monsters" because Chef had finally stopped the 24/7 entertainment circus and put down a few ground rules which were minimal at best.

She enrolled them in every sport or extracurricular activity known to mankind even though they are all failing because of truancy and failure to do homework or class work.

The BM had no expectations for these three kids and they had no accountability or consequences for any bad behavior.   It was all blamed on the divorce.  She got them all IEPs which did nothing because IEPs can't help laziness and permissive parenting.  It was quite embarrassing to see OSS at sports events high kicking it up for laughs and attention while at the other end of the field his teammates were formulating strategy.   Also ginger corpulant OSS screaming out "I HATE YOU" to Chef at a giant intramural wrestling event held in a huge gymnasium while turning reddish purple with rage in his orange wrestling thong, rolls of fat quivering, is an image burned in my brain forever.

Then there was tomboy SD that was constantly shooting toads in the eyes with a BB gun and torturing my two cats but claiming to be an "animal lover."

I don't know how you ladies do it with "ours" children!

Or do they all read from the same script like the HCGUBM's do?

. I personally find my SO's kids' behaviour shameful- they are destructive and act like complete ferals in nice restaurants, other people's homes, museums etc. I would not dream taking them to a theatre, as they'd have no issues acting like halfwits making stupid noises during the show and laughing about it, completely unperturbed by how idiotic they appear. 

When I brought it up to DH his excuse is that he doesn't feel that SS is getting anything from it.

Your main problem here is DH. Semi entertaining SS's behavior, not realizing that toddler tantrums are not appropriate, is setting up a teen age life of misery for all. SS was not getting anything from it because DH was, and is, not accepting the reality of SS's behavior and working to correct it.

"That's how I know step parenting is rigged. We're expected to BE a full fledged parent to SKs, do it all unconditionally, but are not respected and undermined."

Yes indeed. You mentioned he went for a summer visit to his BM. Is he with you most of the time? If so, it makes it hard to disengage without living daily with the consequences of how he is "un-parented" or parented into these bad behaviors by your DH and your in-laws. 

You mention being worried that your bio-kids will behave similarly, but with you as their 100% of the time parent, that is unlikely. As far as therapy, it sounds like SS needs therapy but also your DH. To learn how to parent. If things are how they sound and you have SS near fulltime, and your DH and his parents allow and even encourage this behavior, it's going to suck. Maybe couples' counseling can help you both get on the same page. A lot of parents and grandparents don't realize it but they are actually training their kids to behave badly by giving in to tantrums and unreasonable demands. 

On a way gone SParent community long before I found STalk one of the members had a blended family with two unrelated sets of ADHD/multiple syndromes of the moment who were much like your SKid.  Though your kid does not seem to escalate to violence this SM had one or more of her own and one of more SKId who would not infrequently escalate into violent melt downs.

She was the SAHP while her SO was the earner. She kept all of the kids from doing themselves and each other in.  She was struggling with ineffective behavioral modification support, etc, etc, etc.

I tossed out a from my hip suggestion. It struck me that the goal was to break the meltdown cycle and stop it from progressing to self harm and violence. My suggestion was ice cold spray bottle to the face when the behaviors reached a point of intervention.

Apparently, according to that SM, it worked wonders to end the melt down and progression.  It basically short circuited the brain and shocked the kid into a shocked "frozen" state and she could then direct them to their room and avoid the rage, self harm, and violence.

What would break the cycle with this kid.  I am of the mind that you and everyone else avoiding the kid, it is better to isolate the kid from everyone else.

We have friends we were very close couple friends with.  I had gone to Undergrad and Grad School with the DH the DW was also a Grad School classmate.  They have two on the spectrum boys. One in his early 20s and in his first year of university. He took a gap year after HS.  The other in his mid teens. The eldest was hell on wheels and extremely violent. He nearly killed her a couple of times when he attacked her while she was driving and nearly killed his younger brother any number of times.  They were coddle and comfort parents to the detriment of their safety and the safety of both of their children. 

We were invited to their home for a wine lunch. They did nto do a lot of social things in public due to their boys tendencies to lose their minds and go into the screaming and physical melt downs.  We had been there a few hours when he full on punched me in the nuts.  I grabbed him by the scruff of the neck, put him over my knee, gave him a few swats to the rump, stood him up in front of me, told him that he would not ever do that again, and to go get a book and bring it to me. He brought me the book, we sat on the sofa, and we read the book together. Talking about it, I would purposely read something wrong, he would correct me, we had a good time for an hour or so.  Never again did he lose his mind when I was around. When we would arrive at their home or they would arrive at ours he would get a book or ask for a book and he and I would have reading and book discussions.  This went on for years.   The last time we visited them was about 10yrs ago.  They had moved and we had been overseas for years.  He was about 15 at that time.  When we got there and the hellos and hugs were done, he approached me, showed me a book he was reading and asked if I had read it.  We sat and reviewed and discussed the book for a couple hours each day we were there 

Unfortunately they divorced.  He was chronically under-employed and she is a rock star bank executive.  He to this day remains mad at Doctors for constantly telling him that as he puts it "there is something wrong with my children", She gained contact4 with reality and has gone above and beyond to maximize the opportunities for her on the spectrum young men to have as normal a life as possible.

They were shocked when I put their nut puncher over my knee.  She recognized that as a watershed moment where they saw a direct consequence that broke the overstimulation meltdown progression followed by a calm highly directed activity seemed to work.   The eldest is likely highly medicated but he is mainstreaming, living on campus, at a university a several hour drive from his parents.

I am no expert, but I am also completely convinced that direct intervention in crap behavior, even for the syndromed, far outperforms any tolerance for the behaviors.

See if you can find an immediate end to the intolerable behavior that works.  Water bottle, swat to the rump, get creative but do not run, do not tolerate the behaviors , do not isolate yourself from the kid, isolate the kid from everyone else.  

A very good movie that is an IRL story about a high functioning on the spectrum kid then adult is Temple Grandin.  If you have not watched it, her life is a true inspiration. She had committed parents, then had great educators.  Of course not all on the spectrum or otherwise syndromed kids will have great outcomes. However, mitigating their negative impact on everyone else has to be a key goal IMHO.

So, what might work.  A kid throwing themselves on the floor and pitching a fit might just benefit from a gallon of ice water being dumped on them then made to clean it up once they thaw out.

*unknw*  

He's 7 yo it's only going to get worse. Going uncheck ,, When he goes into his teenage years he could hurt someone.  DH has to get his head out of his a$$.   You, DH, SS. All need professional help to coexist.  With out help your marriage will be over.

Its DH 'S kid and his responsibility to take care of. Not your's.  If DH isn't around. SS  isn't around. You worried aboutyhe safety of your bio kids. I know it's sad