Try placing tin foil, double sided tape, or upside down carpet runners (spike-side up) in the soiled area to further discourage Kitty from pottying there.
They are supposed to draw your pup to them for pottying, but if the puppy has the run of a larger territory it isn't likely to go looking for the pads when needed.
Even if the puppy can't go anymore, this still reinforces where the pottying is supposed to take place.
