I take my Andy anywhere he is welcome. If he did make a mess I would clean it up. Having done adoptions for years at Petsmart nothing will piss me off quicker than people not cleaning up after themselves. Going through the same thing with the other people at the park right now.
Since Andy is a male,neutered but late who marks anything verticle, if we go someplace for the first time he gets a belly band
We are getting better on that too if I make the "no" noise.
How about gifting this woman a basket with cleanup bags, and a book on potty training. if this doesn't get through to her then ban her dog. Not to the car but maybe an X-pen or some such thing.
And having dealt with the after math of some of Ceaser Milan type training.Please look at someone like Victoria Stillwell instead. Takes more time and work but doesn't make crazy stressed out fearful dogs in the long run.
I have a friend who just started her dog training classes and she is awesome with dogs. She is on Facebook MyBestBuddyDogTraining. She is in GA and I am in VA darn it. I have learned a lot from her. Even trained my Andy to come in from the yard when called . He is 10 now when the weather becomes warmer we are going to work on recall in the park.