Hi Monica - there are a number of ways you can set it up. Since the overnight stay covers the dates of both daycare days you can leave the stay dates alone, and just adjust the rate to reflect your price for two days of daycare. Though you can use Rover for a variety of services, the reservation system is clearly set up for boarding/overnight travel sitting in the way everything is worded. However, everything is adjustable, so as long as you and your client are clear on what you want, you can adjust the booking to reflect that in a variety of ways. So long as the stay dates include all the days you'll be providing care (to make sure the Rover insurance will cover you while you are sitting), and the total cost is correct, you're good to go.
If the client is having issues understanding why it would be a different price, you can explain that one night of boarding covers a 24 hour period of time. During that time, you're not only caring for their dog, but you're also attending to any other animals in your care, doing your chores, stepping out to do errands, and also sleeping. The dog is not getting your full attention that whole time (or even most of that time), but is a guest in your home. For daycare, you are present for the entire stretch, and the dog is getting much more focused attention. They're paying for the energy and effort you're putting in, which is far more concentrated for a daycare scenario than an overnight visit.