When I go out in the middle of the night I always try to stem the problem, make everyone comfortable, and then go home to bed and come back the next day during normal hours. I get enough sleep, they don't pay as much, everyone is happy.
Plumber fees are brutal. If I come out in the middle of the night to fix something I have a $100 show up fee. If I'm doing critical plumbing in the middle of the night I charge $250 an hour.