The harder you push, the more she will resist. You've resorted to being so heavy handed and controlling that it's doubtful you will have any credibility with her on this issue for years to come. She's a young woman now, mere months from adulthood. Hopefully she'll learn healthy habits from someone she trusts, because you've messed this up big time. This may sound blunt but it's what you need to hear. Your ONLY option now is to back off and try to repair your relationship with her. No more talk about dieting or exercise. Let her make her own choices and sink or swim, it's totally hands off for both you and your wife when it comes to anything related to food or exercise from now on. The time for controlling her habits was when she was a child, not a preteen, not a teen and not an adult. You either raised someone who cares about her health or you didn't, but the time to intervene is long gone.

Find something you DO approve of about her and support her. Praise her successes at school or some other activity in which she already has an interest. Does she do art, or theater, or sing? Find something to connect with her on and build up her self confidence. Show her that you think of her as more than the inherently flawed object that you and your wife have been treating her like. You only have less than a year before she could legally walk out of your life forever. This is your wake up call.