My child's mother stole her from me about 3 years ago. I am ready to sue her for joint custody and visitation. Is this expensive?

It is difficult to anwer either question, for different reasons.  Normally, fully-contested custody trials are lengthy, difficult, and threfore expensive propositions, but you do not give enough information to actually know what the history is (a three-year gap is huge in the life of a child), what the current facts are, or how to predict what might happen. You also don't provide the basic information necessary to figure out jurisdiction.  Was there a prior order?  Issued where?  Has either parent continued to live in that place?  If those answers are yes, then that place has presumptive current jurisdiction.  If this is the initial action, then it should presumably be filed in the child's "Home State," where the child has lived for the past 6 months.  A better explanation of most of this is set out in the resources posted here.  But you should probably confer with a family law specialist in the place where litigation is likely to occur.