For a crop sensor camera, the 7100 has very decent higher ISO capability with minimal noise.
I think it looks pretty good to my eyes. That is a pretty difficult shooting situation. I've shot some musicals and some plays... that's about the toughest thing I've tackled. I'd suggest to try putting your lens in manual focus mode for sure and focusing on her before you want to take the shot. Then follow her with the camera already focused and try to time the shots where she's at the point in the air where she's about to change direction and come back to the floor.
I can look at your EXIF info so I can't see your exact settings (esp the ISO) but some Nikons do a little bit better at higher ISO settings if you stop down one megapixel setting. That is, use step smaller than the maximum setting. Not sure if the 7000/7100 is like that or not but maybe worth a try.
I'd also suggest if at all possible, partially rest the camera on the back of the seat in front of you if you can manage to sit behind an empty seat. Sort of a makeshift tripod/monopod.
Last suggestion would be to try forcing a slower shutter speed than the camera wants, either by seeing what the camera wants to use, then moving to shutter priority mode and using about three to five steps slower than that (one full stop or almost two stops) or dialing in somewhere between -1 and -1 2/3 exposure compensation. The image will be darker than expected, but sometimes brightening up a darker but clear image gives better results. It's easy enough to try.
And of course, take about 1,000 shots!
Forgive me if you know all this. I'm just throwing out some ideas for distant lower light settings.
What lens do you have, by the way?
Still looks pretty good. When you're some distance away like that, it definitely makes it a bit difficult.