OP, having read through your thread, and most of the responses, I think you are over-complicating things for yourself. This is not to say that this is not important, it is, it's just if you break it down, your options are fairly clear, if limited.
(apologies for the very long post)
Raising your own, useless, grumpy, normal teenagers is hard enough. You grit your teeth and get through it.
These are not normal teenagers and they are also not yours.
It's difficult because you joint-own your home, I think I read that you said that. This is a problem, but if you are not married, it is not insurmountable.
The fact that your partner cannot afford a huge home for his part-time, feral teenagers is not your problem to fix.
The fact that your partner seems to have mental health issues which are undoubtedly exacerbated by the stress of dealing with teenagers is also not your problem to fix, as much as you care. You cannot fix him, he will need to do this for himself.
You won't be able to have much of a relationship with your partner anyway, with all your energy focused on dealing with the teenagers.
All you can do is deal with yourself and your child. It's not an easy thing to do, but it is simple, if that makes sense? Find out what your red lines are, and stick to them. No ifs or buts. No get-out clauses. Yes or no.
Do you want to live like this? (not, can you muddle through the next however many years, stressing all the time - do you want this?)
Do you want your three-year-old to grow up like this? (and learn how to 'behave' from her siblings?)
Is ruining your child's childhood worth it?
Would you want your best friend to live like this?
Can your mental and physical health deal with this kind of life for another seven years? Can your child's?
Do what is best for you and your child. Only you will know what that is.
You will have to change your situation. Your partner will not or cannot change it for you. If he were capable of dealing with his teenagers effectively, he would have done it already.
No relationship is worth your mental health or your child's future happiness.