I don't think you sound horrific OP. A size 18, 5'5 14yo would worry me too. She must be obese according to her BMI? Or at least close to it. That's more than a chubby teen.
While I agree with PP whose mothers have constantly gone on at them about weight despite being a healthy size, who say it's affected them way into adulthood - my mum did this to me too - the difference is that the OP's DD isn't a healthy size, and will need help to get back to one. It has to be addressed IMO, I don't think backing off is an option.
You obviously love her loads, that comes through in all your posts. Do you cook with her? I work with young women, some of who have issues with food/weight, and cooking together can be very therapeutic as as well and fun and educational. It gives them the control over food that they crave but in a constructive way.
Is she into social media, Instagram etc? There are loads of young, cool fitness bloggers like Joe Wicks etc (who is also pretty easy on the eye!) who post amazing recipes, healthy, tasty, filling and easy to do. I know it can be hard to find the time but even just a few times a week would be great - the one on one time and positive attention/reinforcement would be so valuable, as well as the opportunity to learn about cooking and nutrition. She could serve up different recipes to her siblings, make stuff to take to school etc.
Sorry if I'm way off the mark, I just think positive attention, rather than 'punishing' (taking phone etc) might work better here.