Morning OP. I'm so sorry that you're having to go through this. A difficult decision for any woman made 100 x more difficult because of this abusive POS.
I'm going to hazard a guess and say I imagine your partner wasn't the most wonderful partner after your daughter and most likely made you PP worse?
Practical advice.
You need to ring women's aid or domestic abuse charity.
They will take a statement, this statement can either be passed to a solicitor or you can do it yourself
You have the option of many court orders
1 for a non molestation order (so he can't come near you or abuse you if deemed appropriate)
An occupation order - this will ensure that he has to leave the property, in terms of mortgage something like it can't be sold until the DD is 18.
Child arrangements order. Deciding where the child would live.
Or OP. You can ask to be put in a refuge, you might have some difficulty with benefits because you're a home owner but you will still get help.
Also freedom course. - if it is safe to access from home. This will help maybe list some abusive behaviour that you might not be aware of. When I did it it was like a light bulb.
You can do it online.
The website is
www.freedomprogramme.co.uk/online.php
Username - freedom
password - control4me
All lower case. (Can be a bit fiddly)
Good luck. You're welcome to message me.