Please don't put this man on the BC. Firstly, you can only do that if he attends the registration appointment, or signs a declaration beforehand. If he attends with you, he will attempt to brow beat you into using his surname.
If you leave him off the BC then yes, he could apply to court to be added to the BC. There's no guarantee that he will bother to do this though. Even if he does, you buy yourself time before he gets PR. That's time in which you get to be sole decision maker for vaccinations etc. You can also use that time to move to a different area.
Bear in mind the risks of handing over PR to him voluntarily. He could take your baby and refuse to return them. The police couldn't make him return your baby - you would need to apply to the court. If he isn't on the BC, the police can remove the baby and return them to your care.
This happened to a friend of mine. Her ex refused to return her toddler. As he wasn't on the BC he had no PR and the police retrieved the child and returned them to my friend. She was so, so glad she never named him on the BC.
There's also the issue of education, medical decisions like vaccinations but also, heaven forbid, if your child needed surgery, medication or other treatment. He could block you taking your child abroad on holiday to spite you.
I would recommend you speak to Women's Aid for advice. Start creating a paper trail of his abusive behaviour towards you, you may need it later.
I would also block his family members, you are not obligated to communicate with them.
Also, you should report the drink driving. That alone is a huge reason he shouldn't be trusted with your child.