Depends what your paperwork says but if he is behind on child support, he will not be able to claim unless the paperwork says he does get to even if he is behind on child support. Call your local child support office and ask them, they usually have access to your file and can tell you.
WI is an at will employment state. You can fire someone for any reason you want as long as you don't do so for a discriminatory reason (age, race, religion ect). You can also contest unemployment based on her behavior.