What would you do?

I would give her a departure time for the last evening that works for you. The best way to resolve it is to speak with your client, not text, so any advice we give you would also have to be discussed with her.

Rover typically handles overnights as a 24 hour period, so when she requests dates I would simply reply back something along these lines "Hi client, I received your request and am excited to care for fido again. To summarize care for fido will start on such and such a date at 7am and ends on such and such a date at 7am. All overnight stays are for a 24 hour period, if any additional hours are needed after that I also offer a daycare rate of $$ that would be from pick your hours, but keep in mind those will always be the hours this client will expect".

As Walt mentioned I would recommend calling the client and having a conversation, but only AFTER you've decided exactly what your hours will be, how much will be owed, and then you're simply giving information for her to accept or reject. I'd highly recommend against letting your client choose when you leave and at what rate they'll pay for it. It also helps to have all of your decisions in writing first, in case the client flips out and tries to get rover involved.

Honestly, you may lose this client. Or you may not. But trust me you don't want to keep a client who thinks you have nothing better to do than spend your life at their house when it's not needed. And if you're going to be there almost around the clock, you need to be compensated for that.