I would not even interview.
If your rate is $52 per day, I guess that is what I'd expect you to charge. She is taking up the day so must pay for it.
Do you intend to go to hourly? That is a giant leap backward. I don't recommend it. Parents willing to pay full time are uncomfortable with providers who take hourly kids. They want less turnover in the classroom and stability.
Getting everyone to full-time enrollment only is the goal. Anything else is moving in the wrong direction.