My daughter had the same issues - she absolutely REFUSED an NJ tube (which goes further in than an NG tube - to the jejunum, the small bowel, so has to be placed by interventional radiology). An NJ tube has to stay in all the time and she HATED it. It was uncomfortable and she did not want to go to high school with it.
She fought it and fought it and got down to 82 lbs - about a 25 lb weight loss. She was so underweight, we were told her organs could start failing if she lost anymore.
She was basically unable to do anything - forget school, she was pretty much in bed all day.
She developed Refeeding Syndrome (which can cause fatal arrhythmias) and electrolyte issues that lasted for months.
She was seeing a psychologist and eventually she understood that she was very severely malnourished and there was no way she was going to be able to gain weight without the tube. Her psychologist was a huge help with getting her to accept the tube.
Hearing and understanding how serious being malnourished can be was also a wake up call - when she heard from multiple doctors how it could affect her organs, she agreed to the tube.
Her GI also insisted she needed the tube, but that seemed to backfire at the time, the more she insisted, the more stubborn M got. M was 18 at the time, so all the decisions were hers to make.
I would definitely see if there is a psychologist your GI recommends. And I would ask the GI to talk to her and explain why she needs it.
Since she has an NG tube, I would also see if she'd be willing to insert it every night. My daughter did not mind the NG tube because she could insert it every night and pull it out in the morning. It was thinner than the NJ tube and more comfortable, and best of all, no one at school had to know.
It was MUCH easier than she expected it to be. She could do it in seconds within a week.
Her GI did not really give her a choice - the choice was either drinking the shakes, which she tried and could not do, or a feeding tube. It was like medication - not something she got to negotiate with.
Of course, all that changed when she turned 18 and could negotiate everything
but you have a few years before that happens!
I would try to find out WHY she hates the tube and then figure out how to help her deal with it. We may have suggestions...