"I told her that he has scheduled feeding times (I used to have one of those gravity feeders and he would just eat until he's sick and was getting to an unhealthy weight, vet told me to feed him on a schedule) and always has water and snacks available inside. I only ever put him out for 20 minutes and have a timer for it because I'm forgetful and wanted to avoid him being miserable or lonely."
OP, don't even stress over this Karen. you sound like an excellent dog parent and when push comes to shove, she was in the wrong here. She literally ordered her kid to trespass on your property, which is cause enough for legal action.