Forgive me if this makes no sense, have DS2 off school and had to have our pet pout to sleep early this morning unexpectedly so a bit emotional. but I really wanted to offer support.
What you said really resonated with me. I never felt good enough. My father left my mother when she got pregnant and she abandoned me when her new boyfriend couldn't be arsed with a baby. I realise now after many many years that it is them that aren't good enough. It is your mother who isn't good enough to call herself your mother. YOU are more than good enough.
I had a few boyfriends who didn't treat me so good. I stayed as didn't want to be alone. A shit one was better than no one. Then DH came along and he is nothing like they were and I realise how good it can be when you are with a decent, kind, supportive partner. twunt isn't even one of those things.
Your DD may be playing up but you still need to implement boundaries and consequences.
You can do this. You are doing this. Do not give twunt or your mother any more chances. They have had far more than they deserve.
Concentrate on resting, the children, preparing for your interviews and getting the legalities sorted.
You are not weak for wanting it all to work out with him but if you go back you are willingly going back into an abusive situation and you know that is not what you should do, what you want for yourself or for your children.
Ask for any help you need on her. There will always be someone to support you.