Most of the Dells area motels have water parks. You may have to pay for a room but then you would have place to shower and change clothes. Also check out the Adams/Freindship area, there are a few public swimmining areas there. I don't know how clean the lakes are though or if they have showers. Also check out the Green Lake area, Green Lake is very clean but also very deep about 500 feet at it deepest point. Contacting the Chambers of Commerce for ideas works too. Look on a map to see which cities you will be traveling through and contact the Chambers in that city.
Be careful of Perkins they have MSG in a lot of their food, IHOP, Mc Donald's, Arbys, Burger King and Wendy's do not.