Hi, Anita!
I have found that is easier to keep client conversations on Rover, just for ease of access (I can pull up everything from the app, my computer, etc.). In the event of an issue during the stay, keeping the conversation on the Rover thread also allows Rover's support team to more readily assist since they can access the entire conversation on their end.
That being said, some clients do not find the app or website easy to use. If your client has not synced their Rover account to receive text messages, you could offer the Rover Support number so they can guide them through that process. This makes it seamlessly available through their phone, and its just like texting you through any other number.
If she just needs to have a quick conversation regarding something, it might be wise to just send a recap of the conversation through Rover to make sure there's a record of it: "Thanks for making some time to chat today about Fido's care. Just to recap, here's a little summary of our call..."
Obviously, recap messages won't be feasible if she ONLY wants to communicate through her personal line. If you are not comfortable with that, just say something along the lines of, "I appreciate you expressing that to me. I do prefer to keep client communication through the Rover platform, as its easier for me to access from other devices and also allows Rover's 24/7 support network to access our thread in the event of an issue during your booking."