How awful for you! I'm sure you are not the only one that thinks she is crazy. It is so frustrating to care so much about her future and yet be unable to stop her making what will most likely be a big mistake.
Gout isn't the only disease that can arrive with stress, so be happy that you have done all that you can for stepdaughter, and for the sake of your 16 year old, (who will undoubtedly learn something from this)start looking after yourself by going with the flow. Make up with the girl (you are the adult, she is obviously still a child mentally)and be happy. Drink to her happiness everyday with Apple cider vinegar (how appropriate!) You've done your bit. Que sera sera.