Hi B.,
My son had the same problem, they are night terrors. His pediatrician said this happens to some children when their routine is thrown off, especially missed or late naptime. It generally occurs within the first 2 hours of bedtime and it's like clockwork, every night same time. Sure enough, she was right. My son grew out of them around age 3-4.
Generally, kids grow out of them by age 12, per doc. We did everything, even leaving wedding receptions, to make sure he stayed on his schedule after we found out the problem. It's very scary and disheartening at first but once you put a plan in action it truly works and everyone gets a good nights sleep.
Don't wake your daughter up, although she may appear to already be awoke. My son kept his eyes open, sweat, cried, and thrashed but I would hold him tight in my lap, rock him and recite our daily bedtime prayer over until he fell back to sleep. He never remembered a thing in the morning.
Hang in there because the end is in sight, just establish a routine and stick to it, regardless of the greif you may get from leaving/missing events; an evening free of night terrors is priceless. Best of luck.
H.