Best thing you can do for this poor baby is have it adopted out from birth.
Bringing a baby into this irresponsible mess is just cruel.
Obviously, I don't know what your chronic health condition is, but lots of people still do work with chronic health conditions, not because they want to necessarily, because they have to, to keep a roof over their heads. I do find it odd that you say a pregnancy and a baby isn't affected by your health condition, yet it means you are unable to work. Babies are hard work physically and mentally, do you realise that?
This whole situation is a complete mess. You really should have been more careful to not bring a new life into this. You need to do everything you can to protect your baby, go to the council for help if needs be. If your boyfriend won't leave the house and rent privately, then you'll just have to leave on your own and get help elsewhere. As others have said, he's unhealthily enmeshed with his mother, so I wouldn't be relying on him to support you or your baby.
In terms of paying everything for her house, of course, she's not living in it, so the costs should be covered by those living in it. If you don't like it, you both need to find a rental property, even a one-bed flat would be enough for a couple with a baby, and just go non-contact with the MIL. If he's working, he can pay rent, you don't need a council house for that, and then you can also claim whatever you're entitled to for your condition and baby, although, I really do think it's irresponsible to bring a baby into this when you don't seem to be able to afford to. You say you can afford the baby, but how when you can't afford to house yourselves??