This may sound like a strange suggestion to you (and to quite a few on mumsnet unfortunately), but does his Mum live near by, and if so would you trust her to look after your baby? My DDin-Law relied on my husband and me a lot when our Grandson was a baby, up until he started at school. She is a SAHM, also with mental health issues, and our son worked long hours, six days a week because they needed the money. Obviously we were really happy to help when we could (well my husband had to do all the physical help because of my disabilities, but he and our Grandson absolutely adore each other!)
Anyway, what I am struggling to say is, could you ask your in-laws for help, as you don't have any suitable relatives near by? Our son and DDin-law are divorced now, but we get on well with our DDinLaw, and of course we still help out where we can.
Apart from that, please leave him OP, he sounds horrendous. I found that once my DxH left me, so many more opportunities actually opened up to me, like organisations for single parents, even a local CoE Church offered help, and I wasn't a Church goer. But that was 30 odd years ago, so I won't give any names as they may not be relevant anymore, but I am sure that there will be others. Stay strong, you can do this 💐