Well then, how come "My sister & I are going to the movies" doesn't sound awkward?
I think, since "she are" would sound awkard, it is prefarable to use "she" at the beginning of the sentence.
X and I version is correct, and the other way round would not be.
To my knowledge, I don't think that the same applies to She and X, X and she when it comes to the correctness. So, with some simple logic, for the sequence, since being correct is not the issue this time, we could pick the one which is mostly heard as the natural.
And, It sounded awkard to me, but not to you. So, it's best to wait for a native-speaker's comment.