How much should I charge for overnight sitting?

Hello again! I just wanted to know how to charge my family for an overnight stay while they'll be at a concert. I don't exactly know the times yet, but I'm assuming it would be 6pm - 8 am at the earliest. My usual rate is $18/h, so do I charge them by the hour? Or do I charge a flat out rate? I love this family so I don't want to overcharge or anything and I dont mind staying by any means.

Additional info: 2 kids, ages 4 and 2. I've been with this family for about 3 months now :).