All i'm saying is this generation now eat crisps and chocolate daily, they are not healthy foods by any stretch of the imagination. My kids have both but on occasion and they aren't part of our weekly food shop. They aren't restricted, neither encouraged. They don't have pudding unless it's fruit or yoghurt. But will have pudding if we eat out, a special occasion or say we've been baking.
I only mentioned the veg thing because I am a vegetarian but of course someone who ate meat would add meat to those dishes and a side of some sort of carbs, I just don't eat meat. My kids do but only a few times a week.
All i'm saying is that if you battle her on this she will become secretive. If you allow her to eat healthily and cook with her she's more likely to actually eat the food having known what's gone into it.
I'd rather my child eat healthy balanced meals and cut out junk food than shun eating all together because they feel that the meal is too unhealthy/full of fat and become really uncomfortable about meal times.
I think you need not focus on her size i've been a size 8 and lived off of sugar and crap as teen and am still a size 8 as an adult i've continuously improved my lifestyle and now live off of veg, fruit and healthy grains as an adult. I still have treats but in general my diet is far more restricted now but I'm far, far healthier.
The thing with clean eating it isn't a diet, it's a lifestyle choice, to eat foods that are designed to fuel the body not fill it with empty calories and chemicals and excessive fats.
I would talk to her and say things like 'low carbing' or faddy diets aren't sustainable and will male her feel worse in the long run. But a 80/20 clean eating life style is. So 80% of the time you eat good food that has been cooked, doesn't contain a list of ingredients and has nutrition benefits to the body. and 20% of the time you can eat ice-cream, chips, popcorn at the cinema etc. That's is sustainable.
I think talking to her like an adult is important the way we fuel our bodies is very important and I think no matter how old or young you should have some say in it. If she doesn't want to eat pudding then she doesn't have to but suggest she can eat some fruit & honey, granola, or a smoothie, apple slices spread with peanut butter all which are fairly high in natural sugars & calories but not processed sugar. This way you can make sure she reaches a decent amount of calories a day without them being crappy empty calories.