Okay, I didn't read the responses but I may be odd man out here.
My daughter is 8 and in her 3rd year of competitive dancing, but her first year being a part of the big show troupe. If her group didn't make finals she would be devestated. If she had friends going because older and younger siblings were involved, and my parents would foot the bill if I couldn't, I'd absolutely let her ask them.
This happened last year with us, but my daughter was okay to stay home...and it was the parents that opted not to do the competition, not the girls performance. Either way, had she asked to go, I would have offerd food money to send her with a friend (since they already had to pay for gas and hotel). Make sense?
I think at 11, it's very difficult to find your place and if her core group of friends are doing something that she was counting on being a part of, it's going to be hard for her not to go.
As far as going over her mom, mom needs to put her foot down and let her know who is boss. A firm voice and talking to my daughter on the same level (me bending down to be at eye level with her) works well.
We have also drilled into our kids from day one that our rules are our rules. If we say no, no it is.
Now if we're at grandma's and she says yes to ice cream, no big deal. But a big thing like this? Grandma and granpda should have enough respect for mom to back her up.
But I think mom needs to let her go if it's at all possible.
One more thing...mom is doing a bad thing by threatening to take away Christmas. No parent would really take Christmas away from their kid...so it's an empty threat and probably a big reason why J acts the way she does.
Good luck to all of you!