Client booked for incorrect amount of time? Am I to blame?

If I'm interpreting this right, she sent you the first text on Friday morning Sept. 11th and only 1 night was booked, no additional time extensions were submitted. In her text when she casually asks you to take them out out around 7 - 8, she's actually referring to the morning of Sunday Sept, 13th. That should have been booked at 2 nights of care (Friday AM start time through Saturday same approx. AM start time and Sat that AM time through approx. Sunday AM).

Ideally, before both her & you clicked book it now or at any point one of you realized it would have been more than 1 night, the booking could and should have been modified. If there's any difficulty doing so, Rover support will gladly help make it happen to account for all the time.

Since no negative review has been posted yet, I'd suggest you use the rover messaging to send a friendly update, along the lines of hope the pups are doing well, sorry again that we has a misunderstanding in the text messages, and it wasn't clear to me that the end date had changed to Sunday because only 1 day was booked, and each day covers up to 24 hours, so extending the booking through Sunday morning would have resulted in an additional charge. Clearly state something like, I'm chalking that up to a learning error on my part and not asking for any additional compensation and (if you want this person as repeat) look forward to seeing the pups again soon.

At this point, you could let Rover support know by calling them and telling them you didn't realize from that vague language that she actually expected 2 days of care for the 1 night booking and you didn't collect any additional compensation for your time. Chances are they will advise you to not respond to any negative review comments in order to not escalate the situation. If she blasts you with a review, keep you reply short and professional - again something that expresses you're glad that you got to spend time with the pups and are sorry that there was misunderstanding, that each booked night covers up to 24 hours.