My daughter was also very underweight. She tried drinking the shakes but couldn't drink enough to gain weight or even maintain her weight.
Eventually her GI insisted on an NG tube. My daughter learned how to insert it in one day and would insert it every night, do the feed overnight and take it out in the morning. That way, no one at school had to know. The first night was uncomfortable, but after that she quickly got used to it. Within a week, she was inserting the tube in less than 10 seconds.
Our GI insists - for underweight kids, they either need to drink the shakes or use a tube. It is the only way they will gain and grow properly.
My daughter became severely underweight and severely malnourished before she finally agreed to a tube. She was so underweight that doctors were worried her organs would be affected.
The tube was the best possible thing for her. She even agrees now - says it's WAY easier than drinking shakes and she'll never go back to drinking.
Your daughter probably needs more broken down shakes - which ones has she tried? Peptamen Jr or Pediasure Peptide would probably work. Or if she needs elemental shakes, then Neocate or Elecare.
The tube is tiny and flexible - like spaghetti. Kids do very well with it. It's definitely something to consider if she won't drink the shakes.
My daughter gained over 25 lbs with the tube and is no longer underweight. She has much more energy and she feels great. She couldn't believe how much better she felt once she started getting a good amount of calories.
There are Youtube videos of kids inserting their own NG tubes that you can show your daughter.
Good luck with whatever you choose.