I'm actually going to go a little differently than most but with a caveat and say both.

Because she was actually the child (grown or not) of a guest, or a guest of a guest and DEPENDING on the jokes themselves, I can see how she might have embarassed her mother. It was unwise and maybe not the best way to handle the situation.

That said, I absolutely agree with the sentiment and the awkwardness she felt. Guests should be guests, not free labor, as other have pointed out. I'm rather taken aback that the mother wasn't embarrassed by her friend as well. It's bad form to invite people to a social gathering with the expectation that they work or host themselves, counting on social awkwardness to get them to fall into line.

If it had been me, I would have handed my car keys to my daughter and let her leave. Actually, I probably would have bugged out with her. Certainly, as an adult, I would expect my grown child to feel free to bug out with no guilt or shame or awkwardness so there would have been no need to crack questionable jokes to relieve tension.

Then again, you know... there's a good chance this is a standing yearly party and things just went as they always do. Everyone knew what to expect, in which case Mom dropped the ball by offering up her adult daughter as free labor without either the daughter or the friend knowing the real deal. If that's the case, she should just be mad at herself and not her daughter.