Great that you have a legal solution
If you were not able to do it that way, as it is so late at night, I would just bring all three in the room. If it is a motel with an outside door next to the parking lot it is easy to do, but not so if it is a large hotel with lobby entrance. Then the hiding in a purse/ bag plan has to be operated, LOL!
You could always then just take two out at one time for potty.
I have never had a hotel or motel ever ask questions about my dog or wish to see him.
Good luck and have a happy vacation with your furbabes.