My wife had a child with another man. He told her she has to stay in Indiana when he is from Ohio and leaving for boot camp. So my question is does she have to stay since he is leaving I'm in the military and trying to move my wife to where I'm at.

No, she doesn't have to stay anywhere if she doesn't want to. But the real issue is whether she can take the child with her. And she can unless

there is a child custody and visitation order giving him visitation rights; and
such visitation would be adversely affected, if the child were to move.