I have 2 children with this women who falsley claimed I threatened her and had a order of protection filed against me, my visitation rights were terminated. I'm such a threat but she went to court and filed for visitation again, I recently found out she moved my children to a shelter I didn't know anything about this. She was living with her mother and has no job, and no bills, her excuse for moving to a shelter is to find an apartment. Can I charge her with contempt for not notifying me that she has taken my children to live in a shelter.

Yes if it states on your paperwork that she is to notify you of any change of address. A shelter counts but that should have gone through a 3rd party because giving out the address to a known ( safe house ) shelter to an abuser is illegal in most places. Im not saying you did anything Im just saying there is an order in place so it must be honored until it either expires or is overturned ( impossible in some states ).

What kind of custody do you actually have at this time ? Do you have any visitation at all ? Even supervised ?