Just read your whole thread, wanted to say you are coping amazingly well especially with two small children and one still bf.
Your H is an absolute cunt (and I don't use that word either). He blamed and gaslighted you, tried to make you the one responsible for the split and all because he wanted an OW (and he has most probably shagged her, men tend to want to try the goods out before they decide to leave). Then within a day of being found out he was in good enough spirits to go to the pub!
I know it's difficult to see this right now but he is not worth your tears. No one who has seen the struggles your DD's have been through just to live and how much this has effected you and can still put their cock before their family is worth your sorrow. Unfortunately you will feel like this because in a way it is like a death, you will mourn the loss of the person that you thought he was. However he is not that person and has proved that by his annoyance that you're not playing along with his script. No doubt he thought you would beg and plead for him to stay, for him to come home, that would have been a nice ego stroke for him and it is probably pissing him off that you've not done that.
Just keep getting through one day at a time and it will get better. I found that box sets got me through the first month, I would put a DVD on and when I was completely knackered I would fall asleep but since I was only sleeping a couple of hours a night when I woke up I could just carry on watching. I moved on to audio books, I just set it off and listened until I drifted off and when I woke up I didn't have to deal with my thoughts just listen to the story.
If you feel sick ginger biscuits and ginger beer are good for helping tone down the nausea and eating bland stuff in small portions helps. Porridge is good for breakfast, poached egg on toast for lunch, anything high protein and easy to make.
Don't worry about leaning on your family right now they would rather you did that than struggle and possibly have a breakdown. Oh and yes, no matter how sympathetic you mil is she is still his mother first. She will defend him so probably best not to talk to her about him ATM.
Do go see a solicitor ASAP to see how you stand. Take as much financial information as possible and ask what you should do about finances. ATM he is being reasonable but that won't last. Once he has to rent somewhere to live he will start saying that he can't afford to give you as much (their guilt fades amazingly quickly) and he will start to blame you. It will be he wouldn't have done it if you hadn't done 'x' or if you'd done 'y' everything would have been different.