You've had a terrible year, without a doubt.
I think you have to suck up the fact that you have to stay with your mum. You absolutely can't expect to apologise to your dad and step mum then move back in with them - that is hugely manipulative and as bad as the things you have done for all these years, imo. A sincere apology, and then REFUSE to move in with them even if they offer, seems the right way to go.
I would also, long term, seek to repay the deposit money that you extorted from your dad. I doubt he will accept it back, but that would be a good ambition.
You can spend the rest of your adult life eating humble pie with you step mum, and trying to be a better person. At least you won't bring your DD up poisoned against her, that is one benefit.
Apologising to your step mum, openly, simply and with no expectations, seems like a good first step. And then apologise to your dad too, as you must have been hell to live with, and even in the years since.
It will take time to get back on your feet, but presumably your ex is still paying maintenance for the baby so that will help a bit?
Don't reject the offer of the neighbour helping to babysit. You may genuinely find it helpful, to speed up getting back on your feet. Get to know the neighbour well first though, if you don't know them already (and maybe have a private chat and offer to pay for the help, if they refuse payment a box of chocolates and a bottle of wine would be kind).
It does sound as if your mum might have some good intentions, but goes about it very badly. Putting you in the attic room means you can be noisier with the baby without worrying about disturbing her. Insisting on fixed mealtimes with you is a bit much, but perhaps she thinks it is important to spend some quality adult time together. Deciding the days you can use the washing machine will ensure there is no confusion and room for argument. As long as you have enough baby clothes (hello eBay Used clothes bundles!) it is manageable.
If you haven't lived with your mum since you were five, and somehow she got wind (from your siblings?) what an indescribable bitch you have been to your stepmoum, perhaps your DM has reservations about sharing a home with you, and wants it on her terms.
Try going in with kindness and patience and a sense of humour, try to abide by her many, many rules - perhaps if you do this, she might eventually ease some of the restrictions. Having rules and boundaries will make it easier to share a space when neither of you aren used to doing so together. You sound very hard to live with and your mum is probably anxious and braced for many fights and you being completely contrary. Her controlling behaviour may just be a way to defend herself a bit?
Sometimes hiting rock bottom really does make you bounce back up, so be strong and hopefully soon you will be back in full time work, perhaps your mum and neighbour can help with childcare until you can find and afford a full time childminder and full time work.