We carry a potty chair along with small powder scented plastic bags to line it with in the back of our van at all times. It has come in handy at the neighborhood playgrounds as well as for long trips. Especially long trips. It never fails 5 minutes after a rest stop my 4 year old daughter will say, "Mommy I have to go potty". So instead of looking for a place to stop we just unbuckle her from her car seat and set her on the potty. When she is done I just tie up the bag and dispose of it in a trash can at our next stop. Don't worry your daughter will stop touching everything in the public restrooms soon.
Hope this helps.
L. S.