OP I'm so angry for you!
There is absolutely another woman from what you've put, and I'd not be chatting to his mum going forward from what you've said. She's not going to be helpful regarding him and it sounds like isn't a great grandparent role model for your kids either.
It's so hard for you right not with two little ones. Get legal advice about the house and child maintenance. Chat to your health visitor or midwife about your concerns on his parenting. Ask them if there is any local support you can access, there are often support groups and service to help mums of young children but they will vary area to area so it's worth asking those in the know locally.
I'd consider keeping a log of when you have offered him time with the kids, if he's bothered, and how the interaction went. Just dates and facts, nothing emotional but it may come in useful down the line.
I'd offer some set days and times each week where he is welcome to come round and parent while you have a bath, get on with household stuff if he turns up. If he does this gives you a bit of time while keeping an ear out. If he doesn't, he doesn't.
Don't continue to communicate with him or his mum on a emotional level. Only discuss kids and anything about the house or finances with him and I'd just not contact his mum unless you absolutely have to.
I'm so sorry. You will get through this and in the long term it sounds like you and the kids will be better off without him.