8/13/17 Note: This is a complete change to my former answer.
I was very confused about all of this, mostly because Rover has no way of knowing when a stay begins and, thus, has no idea when 24 hours are up, so made my own call to Rover support and spoke with a nice person named Jen.
Here is the answer:
1 - We are absolutely allowed and encouraged to charge daycare fees for a stay that exceeds 24 hours. Our time is valuable and it's only fair.
2 - HOWEVER, insurance goes by CALENDAR DAYS, not 24 hours from start of stay. So, if a client drops off their pet at 8:00am on August 1 and picks up at 10pm on August 2, that is still 1 Rover Day and would be covered by insurance. It's up to you whether or not to charge for the 14 extra hours.
3 - Currently there is no way to add daycare fees to a booking; it must be done as a separate transaction. I mentioned to Ms. Jen that this is cumbersome, that a line-item should be added to the original booking page so additional daycare fees could be transparent on both sides. She said many people have suggested this and that she has sent all those suggestions 'upstairs.'
4 - To include daycare, both parties should discuss, in advance, drop off and pick up times and the fees associated with extra hours. The manual adjustment toggle should be used to increase or decrease the total charge for the stay.
I hope this is helpful to many!