Hosts are sometimes wary of new users, @Cynthia1011 , so asking questions is normal. If she is telling you right off the bat she doesn't believe you, however, the booking isn't starting off on the best foot. By grilling, you mean she is asking you the same questions over and over?
I would say that if this is so, it will be best to cancel and find a place where you are more comfortable with the host's communication. How much time do you have before you need to take that car in? If you have time, send an inquiry to the host of another place you like the look of. See whether the communication makes that place a better fit.