"She shows no tolerance whatsoever for them being around...  they can't make noise, or have toys or whatever.  She doesn't want to be around them, and I get that they are new... but it is just a werid vibe and I hate it."

Hmmm, that doesn't sound good. I mean, she doesn't have to like them, but if you guys are living together now, she needs to accept that they are part of the household.

She should be kind and civil to them.

How did she think it was going to work? Did you have "hard conversations" about  what the set up would be like? You have 3 young children. Kids make noise, play with toys etc....

As for her son, you have already identiifed that he has problems - sounds as tjough there are safety issues with the other children.

Maybe go back to how you were? Separate households and date each other, probably the best and safest solution.

This all sounds like way too much, way too fast. You say you are a widow with 3 kids, one of whom is 3? Big loss, big change. Your SO has a child with severe emotional and behavior problems. That's too much for your kids to deal with. Your SO also seems to be having issues with your kids. It may be nobody's fault, but maybe dealing with her one disturbed child is too much, on top of 3 kids who recently lost a parent. Maybe dealing with her child is too much for you, with everything on your plate? 

Her not liking or wanting to be around your kids is not right. As a BM and a SM (although I don't refer to myself as that anymore), when I met DH, I did everything in my power to be kind to his kids, show them love and acceptance, etc.  Granted, 3 were adults and the last two were 12 & 15, so I wasn't trying to be a "mom" but more of a friend or aunt. What your SO is doing is very troublilng, with the reasons you stated on why she's acting like she does. 

As for her son, his diagnosis does not give him a free pass to behave as you describe. I have several friends with kids diagnosed with high functioning autism, as well as one who has THREE severly autistic children. ALL of those kids are well behaved because their parents did the work called "parenting." Your SO is not doing her child any favors.

You ask if it will change. With what you've described, I'd say no. This is how your SO parents or doesn't parent. Her child is 11 years old. Even if she finally decided to starte implementing consequences for his behavior, it's going to take a lot of time and consistency to get him to behave better. Think major melt downs and lots of conflict.

With all that going on....exactly why would you want to subject your children, still grieving the loss of  their mom, to this kind of an environment? Please consider getting back to your own place. You can continue to date but now that you know the red flags, watch for your SO to make changes. If not, you know exactly what you'll be going back into should you consider moving in together again. 

Best to you.

Honestly,  I would step back from the cohabitating situation.  Your kids deserve to be in a home where they are "tolerated".  They deserve to be raised without a disruptive influence.  Neither of you seem to have an affinity for the other's children.

It really is the simplest plan for you to maintain your separate households... date.. have overnights (more when her son is with his father right?).. Then when yours are out of the nest... and hers is.. out of the nest or whatever he can do.. you can rethink living together.  

As it stands right now, it doesn't seem fair to any of the kids to be in the household together.

The best advice I ever got was, "you made a decision. It didn't work. It's not a big deal. Just make another decision." 

I will echo what everyone else is saying... 

Not only is it not fair to you, but it is not fair to your children. Now, you shouldn't make all life decisions wrapped around your children, but you should provide them a safe happy home environment. Not only does her child have major issues, but he also gets a separate (unfair) set of rules. ADD to that, she is not kind to your children (that will be hard to admit, I am sure, since you love her). Kids can sense that - particularly the younger ones. 

Don't give your children a shitty home life and childhood just so you can be not single. 

Being blunt

You have youngins and the woman you want to be with shows no tolerance for your kids. Are your kids well behaved for youngins at this age?

Regardless i truly believe if you have young kids and at the starting gate and your partner shows disinterest I wouldnt progress the relationship.

Blessings

Seperate households. Friends with benefits. I wish you the best:)

Things only stay bad if they are allowed to stay bad.

To follow up "Get your kid under control or I will." When there are protests on how  you parent and discipline her kid, and there will be. "If you do not like how I parent and discipline then step up and get it done before I have to.  If you will not step up then you will have my back until we can discuss it in private. Are we clear?"

Her kid rules the roost. Your dog and your kids not allowed to play!??  Seriously --- RUN. Get your kids and your dog outta there.