How is it possible, with 50/50 custody, that my ex-wife can move to another county without my consent?

Do you have joint custody (equal decision making)? If so, she cannot make unilateral moves on choice of school without consulting with you and your agreeing to any changes in the choice of school, whether in your county or not. There is no law that prohibits her from moving to another county, as long as that county is not more than 150 miles away from your location. Wisconsin's "removal statute" prohibits the removal of the children from the state or 150 miles within in the state from the other parent, unless the parent who wishes to move, first provides 60 days advance written notice by certified mail of their intention to move, with a copy to the court. The notice must provide details of the proposed move and the other parent's right to object within 15 days. If a written objeciton is filed, generally you cannot move with the children as planned unless the court determines the move should be allowed at a contested court hearing. If her move is less than 150 miles away from you, she can technically move; however, (A) she must abide by the joint decision making rules of your divorce decree (meaning no changing schools unless you agree and (b) if she moves, she must still follow the placement schedule outlined in the divorce decree, or she can be found in contempt of court. The third issue that arises from someone moving out of the area is how do the children get back and forth during your periods of placement. If she is the one moving, it is not reasonable for her to advocate that you come to her and pick up and drop off the children anymore. If you are the one moving away, that burden would also fall on your lap.