Sorry you have to go through this....
Make sure everytime he threatens your baby sitter, she reports it to the police and make sure your lawyer knows each time as well...the police might tell you & your sitter they can't do anything about it but tell them you want it on record with them just the same.. The fact is unless he takes action on his threats or doesn't abide by the order of protection, they can't do anything...unfortunately
Does he drink heavily, do drugs or have a police record??If so, tell your lawyer and get proof of this for the judge to see when you go to court. Is there anyone else you know he has had a relationship with that he badly abused who would witness his behavors?
Have you talked to another lawyer for a second opinion...if you feel your lawyer isn't doing enough, you should.
He can lie and say what he wants about you but he has to prove those things are true. I tend to think if he can not prove you are an incompetent mother he wont get custody but will only get visitation rights with or without visitation with supervision.. And if he doesn't get visitation rights, his Mom can as she is the grandma... Make sure your lawyer knows everything about you so there are NO surprises when you are all in court.
Maybe it would help you if you make a list of questions and concerns and go over them with your lawyer. He should be able to explain things to you to make you feel more comfortable about your case...
In the mean time breath...take walks, exercise, which is a good way to re-direct your energy, frustrations and fears. Focus on your work, your baby.....Be good to yourself and work on keeping your spirits up as you don't want to run yourself down.
Good luck and keep us posted....