OP, I am so sorry you are in this position.
It sucks.
You can register a baby and not put him on the birth certificate, and then he would have to go to court to get Parental Responsibility...which would the potentially him having the right to access, take the baby to his parents, etc. Though depending on the SS reports etc, there mighty be restrictions. But essentially - yes one way or another he would be in your baby's life. And , in cases like him, yes, it seems insane to me, too.
OP, hard as it may be, in your shoes, personally my choice would be to end the pregnancy and concentrate on caring for your toddler.
Talk to Women's Aid or any Domestic Violence / Abuse / Women's support agencies and charities you can find. It might be that because your toddler witnessed the violence you will have a better chance against restrictions over access to your toddler than you would over a new baby.
And worrying about the huge financial and practical impact of having a baby and toddler, on your own, would be more than I would choose. Supporting one child with a violent feckless father and violent parents is bad enough - you presumably didn't know that that is what you would have to deal with when you had your first child. But bringing another child into that, supporting a second child in the middle of all that - no.
And as you say, it will only give him more links to you. For years to come.