I would stay for an ice skating party. Kids need help with the skates, the bathroom and it's usually during a public skate. So there are lots and lots of people there. One fall and kid looking for mom is all it takes for the waterworks to start (appropriately so).

I'd stay as they may not have enough help for bathroom, getting skates on/off, etc.

You bring her, get her settled, stay a few minutes to make sure she's comfortable (if she isn't, you can stay!).

Another stupid question.. How does a drop off bday party work?

DD is almost 7 and was invited to a party at a skating rink. Am I supposed to supervise her there? Do I just drop her off? How do I know? I know her parents, but I don't skate.

I've never been to a drop off party. Usually, parents hang around.