I can totally sympathise with QueenB, I found it really difficult to sort out contact with my exp. A court order would be binding, but you would be encouraged to try mediation and work out contact between yourselves before it got that far. Court orders are the last resort.
You can get free legal advice from most solicitors, and if you are not on a high income, you should get legal aid.
You do not have to have exp in your property. My exp was violent, so when I came out of refuge, I had a court order to stop him even knowing where I lived.
He does have rights to contact, but you could try a contact center, or request that he takes the child to a public place. To begin with my exp only had contact in public for a few hours at a time.
It is really hard to allow that contact at first, I felt fiercly protective of my babies and found it really hard seeing them go to an idiot who couldn't look after them properly. It does get easier though, and hopefully contact will be good for all of you. The baby needs time with father, and you deserve a break soemtimes too.
SA - I think you are seeing things too black and white. I can feel for men who do nothing and lose contact with their kids, but women do not always know what the future holds. My exp first hit me when I was 4 months preg. Our relationship had been fine until then.
I haven't ever stopped exp from seeing the kids, but after what he did to me, I wanted reassurance that he was not going to be like that with the kids, and for lots men, dealing with babies without mum around isn't so easy.
Interestingly, my exp's new gf thinks i act out of jealousy and spite, cos that is what exp tells her. She doesn't believe the lovely man she was with could ever hit a women. But I have the medical records to prove it.
Sadly it is a repeating circle, when I was with exp, I believed his previous wife was lying when she said he was violent too. It was only after I left him that I found out his ex wife was still on prozac.
There are two sides to every story.