I really just don't understand this at all. Bat Mitzvah's are very important and sacred events with months, often years, in preparation for them. I find it hard to believe that on such an important day, the girl, the parents and the grandmother's focus is not on the event but on embarrassing two young girls. I'm not saying it couldn't or wouldn't happen, but with all of the Bat Mitzvah's and Bar Mitzvah's I've been involved with, the religious importance of the event, particularly at the syngagogue is what is uppermost on everyone's mind.
If it did happen as you said (and the grandmother was not confused or senile), then I would send the invitation back to the parents with a note asking for exactly what purpose they had invited your niece if they did not want her there and then I would send a copy of that to the rabbi.