This doesn't really sound fair. At 9, 10, and 12, these kids are more than old enough to understand you have a young baby and need them to listen and be quiet sometimes. When I had my son 15 months ago, SD was 6 and able to understand nap time = quiet time coloring or playing in her room. I was up hourly with the baby so I often napped with him while she did something on her own. 

She also knew she had to listen more because if we were going somewhere/had to get something done, it was a lot harder for me to manage with the baby. So if I told her to get dressed, she went and got dressed. If I told her to pack something, she did it. She just knew she had to behave to make things easier for me. DH reinforced it, I reinforced it. If she was causing as much trouble as your skids are, DH would have been okay with me putting her in daycare or with a babysitter. 

I understand one child is on the spectrum, so they may not be able to understand as much as the other 2, but the other 2 are old enough to help you manage the child that's on the spectrum. These children are not being expected to live up to their part of helping run the household smoothly. I believe kids rise to the occasion when expected. 

Don't go back to work. This is your time with your baby. You deserve it. And you deserve to enjoy it. You are on MATERNITY leave, not babysitters leave. If DH can't help you make sure his kids behave and let you enjoy your time off, he needs to put them in some sort of program or back to BMs while he's working. It's that simple. 

It seems like not only are you having a difficult time juggling 4 kids, 3 of which are not yours, but you are getting zero support from your DH. 

Honestly he sounds like an ass. 

If I were in your position I would find daycare for my son and go back to work. Skids are your DH's problem.

Now if he wants to be supportive, that ^^^ may not happen  But while he is an ass you bet your ass I would do just that. 

Time to leave your DH alone with the lot of them, baby included, for a weekend. Go visit your family. He could do with a short, sharp shock.

I don't think any normal person can cope with 3 rambunctious kids who all need attention in their own way, and then a baby on top of it.  To me, it seems it is convenient for your husband to dump the kids on you to care for. Three of them are not yours - what role is DH playing?? Where is the step-kid's mother in all this. 

At 4 months, you really would be sleep deprived. (My son didn't sleep through the night till he was 10 months old and I was sleep deprived to the point I thought I was going insane.) Your body is only probably recovered now from the birth. Being a  SAHM mean you probably get no break from the kids. Unless you can organise some ME-time where you get a break from the kids, it is non-stop.
 

If you feel ready to go back to work, do it. It should be your choice and not guided by anything other than you and your baby's need.  Adults need adult interaction. As much as I loved my son, being a SAHM was actually hard. I was home for two years - and by the time my son turned two, I was more than ready to go back to work! Don't feel guilty or bad if you are ready  to go back right now. Even if you don't and want to stay home with your baby, your DH needs to play a more active role in raising his own kids.

I was a SAHM for 4 year when my bios were little. I loved the opportunity that my exH provided me in being able to stay home with them and will forever be thankful for that time. HOWEVER- I am a better mother as a working mother. Even when I stayed home I was super involved in different volunteer organizations- I even kept an office at one (baby swing and gate to keep in my toddler there and all!). Sure, I wasn't paid, but I worked. 

Once my youngest was old enough for preschool, I couldn't wait to get back to "real" work. 

It is ok to want to go back to work. To have something outside of the house with adult conversation and lunch breaks with friends! It is ok!! 

I was glad to stay at home while it lasted but if an opportunity had presented itself, I would have gotten back to work sooner!

If the older kids are so bored they are constantly bickering and being noisy, time for them to contribute to the household with some chores. The oldest should be doing their own laundry (really all of them). I'm going to give your husband the benefit of the doubt that he's adjusting to being back at work still.

The older kids need something to keep them busy, routine, and to be seperated. Nap time is quiet time, and if they don't stay quiet, they have to clean, go outside or takea  nap too.

1.  You are understandably tired and stressed.  Not saying that post partum depression is in play.. but it could be lurking underneath a little bit and contributing to your overwhelmed feelings.

2.  You have a new(ish) baby PLUS Three older kids freshly under your control.  That is 4 kids vs one adult..

3.  Your maternal feelings.. well.. I have a SIL who is in education but when she had her own child.. she really struggled because she was NOT a very effective parent.  Her kid walked all over her in many ways.. all the way from the start.  Not intentionally in a "mean" way.. but she just was not a very confident person in her role.. the kid sensed it and didn't respond to her well.  So... in as nice a way as I can say it.. you may be maternal.. and had an urge to be a parent... you may not be actually "parenting" very effectively.  It's not hopeless.. but it may come to the point where you decide that being a SAHM isn't the box of chocolates you thought.. and working may be a better alternative than floundering.

4.  Your husband is not understanding because I'm guessing he didn't have these same issues?  Were the kids like this pre-SAHM time?

5.  I think you need to grow a set of parenting cojones with these kids.  Not in a mean way..in a "no nonsense way"  They are all old enough to listen to direction.

When they are being bickering and loud you tell them.. 1.  I am not going to come down there and referee.. if I have to come in and tell you to settle down a 2nd time.. EVERYONE is going to be separated and face consequences..if you have to go in there again.. you go in and sternly tell them.. well, I did warn you.  child 1.  come with me.. and take them to their room and tell them they are to get in PJ's and get into bed.. they are to stay there.. no reading.. no electronics.. nothing till you say so.  Then go collect child 2.. same.. then go collect child 3.. same.  Give them a couple of hours of quiet separation then allow them to come out and remind them that you expect them to be on good behavior and quiet.

When SD9 is being annoying with her "i know better than you act".. pull her up short.  Tell her that her sister does NOT need a running commentary of every thing she does in life.. if that is the game SD9 wants to play.. you will be glad to be more active in pointing out all of HER faults... and mistakes.. of which you notice quite a few.  "roll your eyes" at that point. 

And.. get these kids more active.. tired kids are good kids.  Can they get into an afterschool activity like dance or gymnastics.. they are all girls..something you could truck them ALL to?  Or institute afternoon walks every day.. you pushing baby and the three of them walking along.  Also.. get them involved in being more self sufficient.  They should learn to do chores and be responsible for things like laundry.. vacuuming common areas etc..

And.. try to be more assertive about stuff.. don't ask timidly.. just tell them firmly what you want them to do.  back talk and refusals get consequences.. perhaps no TV or gaming.. going to bed immediately after dinner? loss of privileges etc.. and PRAISE good behavior.  Stroke their egos when they ARE good.. because I'm sure they are good at times too.  "Thank you for being so thoughtful and helping feed baby... thank you for being quiet during baby nap etc.."  Parenting is about fostering the GOOD as much as redirecting from the bad.

I send the older kids to their rooms when it's time to put the baby down for a nap. Which isn't a punishment, that's where all their toys are and SD wants nothing more than to sit on her tablet all day anyway so she just takes it in her room and watches YouTube on it. Do they have separate rooms? 

You'll have to find something they care about enough to get them to listen the first time. So taking away a privilege or electronics etc. Another option could be finding after school or weekend activities for them. Or if you can afford drop in daycare or "schools out" programs at the Y or similar things when they have days off?

"I told him and he said I'd need to do a bit better tomorrow as DS3 starts high school on Friday and needs all her uniforms washed and ironed."

Your husband is an unsupportive ass.  Remind him that three of these kids (the ones causing most of the chaos) are NOT yours.  Remind him that the vast majority of the household expenses belong to him and his.

In your situation, I would forget about being a SAHM and go back to work.  Frankly, I think you're in a big danger zone by not having your own income and your own exit plan.  Not saying you need it now, but with your husband's attitude and lack of support, you may at some point.

It appears that you have rules and standards of behavior for the spawnin your home.  So, quit screaming.  One infraction and  you grab the screaming fighters by an ear, give it a twist, and march each of them to a separate isolated room until you decide they can come out.

Lather, rinse, repeat.  No need to scream.  After they get a twisted ear mach to their isolation space a couple of times they will understand that the screaming and fighting isn't returning any benefit and is actually returning unpleasant consequences.  

Apply escalating age appropriate consequences until you reach the balance point where the kid will correct their behavior to avoid any increase of their state of abject misery.

It works.

Give it a try.