I turned down an invitation when DD expressed she didn't want to go (a child she doesn't get along with) or because of scheduling conflicts. I would definitely seek alternate means of getting there rather than ask people I don't know very well to accomodate my DD possibly getting sick in their car, I agree with PPs that it is a lot to ask esp when they'll be preoccupied with all the birthday stuff. Do you have a friend who would be willing to take you? Ok, it is a bit of a distance, a good
friend? You could pay for gas and find a cafe to hang out in with your friend during the party . I'm not sure I would ask DD until I had a plan because if she says yes and then you can't sort something out, she would be upset, but then again I guess a 7 year old would realize the party went on without her, mine is only 4, if we can't go I can still just not mention the party and she's none the wiser.