Hi there
I'm so sorry to hear you're in such a difficult and miserable situation. Understandably you must be feeling trapped and at the end of your tether.
Have you ever had a DNA test to confirm your paternity to the baby boy? Also, is your partner getting professional treatment for her post natal depression?
I know you feel that it was unprofessional for the police to suggest applying for full custody of your son, but I was wondering something similar. It sounds like it's very difficult for you to contemplate this at the moment as I imagine the trapped feelings are overwhelming, but if he's your son, he needs you.
Have you spoken to your family about how things are at home?
I also wanted to leave this link here so you can maybe find out about further support and options for male victims of domestic violence.
http://www.mensadviceline.org.uk
http://www.refuge.org.uk/get-help-now/help-for-men/
Edit: just to add, I agree fully that you need to be away from her. The violence is physically and emotionally dangerous. It's just trying to find the best way to do that from the professionals, hence the above link.