If you don't trust him in your house because he steals, don't let him in your house. My own son stole from me almost every time I let him in, he was fast and stealthy and I often didn't notice what was missing until he was gone. He once stole a small TV that my husband took with him when he traveled for work, and got it out in his backpack...on the ploy that he just needed to pick up some laundry he had left downstairs.
Trust your instinct 100%.
You are strong and able to take care of yourself and your child. Remember that and you will find solutions that don't include "trusting" him.
Again, I am sorry you are going through all this and send hugs.