Unmarried father; mother left children with father what rights do I have if she try to take my kids from there home.

Have you gone to court yet to establish legal custody? If not that is your first step because other wise you have no legal recourse they are her kids too. You have to get into court asap to have physical custody awarded to you with her having visitation (if she want's it). Then and only then will you be able to have the court hold her for anything about her keeping the children past when she is supposed to.

You have the right to go to court and file for custody.