This is a very frightening, frustrating thread to read.
As someone who was a child raised in a home with dv I can assure you
Your daughter will be aware of what's going on. She wont understand it the way someone older would but she KNOWS daddy hurts mummy, daddy is scary and must not be made cross.
Entirely possible she fears being hurt by him (and she may not be wrong)
Under Clare's law you can find out what REALLY happened with him and his ex. Chances are she wouldn't say to you because
A she's ashamed she put up with it (even though she shouldn't be)
B fear of further reprisal from him not only against her but their child. (completely understandable and possible from the sound of things)
C thinking you wouldn't believe her
D it being distressing to talk about.
I'd also lay odds he hasn't told you the HALF of it. You don't get 3 months for JUST breaking a non mol order! Or at least I've never heard of that (much to my brothers frustration)
He's a police officer and deals with dv regularly. He's working this Christmas and would MUCH rather get a call to help you leave this abusive arse, than attend your murder/manslaughter and have to deal with a distraught 2 year old trying to 'wake mummy' - a type of scenario he has had to deal with more than once.
Shocking? Yes, but happens far too often.
He's heard it all 'he's a good dad' no dad that hurts and/or scares mum is a good dad. 'He's not always horrible' yea cos he's not stupid if he was always horrible you wouldn't stay. 'It was my fault I made him angry' no he's an adult, if that were true he'd batter everyone that ever offended him and he doesn't. He'd also have no problem doing it in public which they never do.
Get him gone or get out yourself. The fact he's calm and 'behaving' just now proves nothing. Show police the huge number of calls, the texts (which I'm guessing would show his true colours) not to mention your wrecked home! That alone will be an obvious indication to most officers.