14. That must be an horribly difficult decision for you to have to make for your daughter. It sounds like you really want the best for her, and I totally admire that. I would be really concerned about her maturity not being ready to have wls surgery. For me, personally, from about age 17 to age 21, hanging out with my friends and drinking, eating poorly, and various other immature things were a big part of my life. If I had had wls before that point in my life, I would have ruined myself because having fun was more important than taking care of myself. I was on Phen-fen about this time and I couldn't or wouldn't make the necessary decisions to follow my doctors instructions and ended up gaining back all the weight and then some over a short period of time. At about 24 or so, I looked into gastric bypass. There were a lot of reasons I ultimately chose not to get it done, but the biggest thing that I realize now, was that I was not emotionally ready and wasn't ready to make the lifestyle changes necessary to be successful long term. I've now made most of the other changes in my life that will now allow me to be successful, I've recently developed triathlon as a hobby, so I'm far more active than I used to be, I've changed my eating philosophy to a much cleaner diet, where 10 years ago, I was still perfectly willing to eat fast food and other garbage. She's got a lot of teenage years and early 20's ahead of her, and that age group simply isn't known for making a lot of responsible decisions.
I'm not a parent, and I'm certainly not your daughter and don't have any way to assess whether she could be ready or not, but if I were to base this decision from my own life experiences, I wouldn't do it. In your role as parent, I would probably try to work really hard to provide the healthiest food possible and try to get her into therapy to see if there is an underlying emotional/psychological reason that she finds it so difficult to lose weight.
Best of luck to you and your daughter. I hope that whatever decision you make works out well for you both.