When you get contacted for a booking, you always need to find out when the client is dropping off and picking up the dog for exactly this reason. You have the ability to modify the bill before it is paid very easily if you ascertain the exact length of the stay. Rover states that one "night" is good for up to 24 hours of care.
If a customer drops off a dog at 8 am,, then you tell them it has to be picked up by 8 am on the last day. If they are coming in later in the day, you determine how much more they should pay based on the overage. Since you also offer daycare, then you can easily send them a request for daycare on the final day, which covers the whole time.
Communication with the customer is key. Not a single customer has quibbled when I've laid it all out for them. You can still get it fixed before the stay begins.
BTW, boarding is not just an "overnight" stay. As i said, it is good for 24 hours of full pet care, including walks. If you don't think your nightly rate covers those "extras," then you should raise your rate.
