Does the mother have full custody of her child till the father takes her to court?

Both parents have parental rights under Wisconsin law. Dad can't simply take the child away - only a court can make placement/visitation and custody determinations, and there is a legal presumption that shared placement and custody is in the best interests of the child. That also means that you can't prevent the father from spending time with the child without a court order.

If the father wants to exercise his right to visitation, the general public policy is that this is a good thing for him to do - unless doing so would put the child at risk or in danger. He does have - as the parent of the child - a right to placement/visitation unless a court orders otherwise.

The father does have a legal obligation to help support the child, and unless you have some reason not to, you should file a motion with the Milw County family court to order him to pay child support. The amount will depend on how much he makes, how much you make, and how much time each of you has the child.

You should contact the Milwaukee Department of Child Support Enforcement. They can help you get started with having the father to contribute child support and to establish the placement orders. You can contact them at 414-278-5160.

At this point you probably don't absolutely need an attorney, but you should get a court order establishing support and placement. If you and the father can agree ("stipulate") to the child support amount and the terms of placement that's great, but that still requires approval of the family court commissioner. If the father doesn't want to cooperate, you may want to consider hiring a family law attorney to help you.