Right - I imagine your cat is responding to the sudden change of a puppy in the home. How old is she? As far as what to do about it, I unfortunatley don't have any suggestions/thoughts - I'm sure some of our more cat savvy people will help you.
As for your puppy, continue monitoring her and going back to step one. Most likely she was allowed to pee/poo in the setup that the trainer had for her, and she's reverted back to going anywhere. It's certainly workable as long as you continue being consistant and patient.