Something no one talks about: every Command Masterchief has a list of "trouble" dependents. They know who they are. Your sailor should talk to his chain of command and his CMC, let them know she may try to disrupt his work environment.
As for her taking the child away, that is a matter for the civilian courts. The Navy can do nothing. If he receives any money for dependents, such as BAH, he must turn it over and support her fully. That only changes if he divorces her.
I have lots of stories, but nothing concrete. He needs to talk to his chain, see what they suggest. He should check out Fleet and Family Services if he is stressed and wants to talk to someone outside of his command.