I would say you need to find a way to get her involved with the positive changes you are making- share some interesting tidbits from your nutrition class. If you have a log of what you are eating, share that with her too.
As a mom, I know it is very easy to worry that your kids will make the same mistakes you did.
As a daughter, I know how frustrating it is to have someone think that just because THEY did something stupid, that YOU are going to do it too!
I just think communication is the key. I know you don't have anything to prove, and you really shouldn't have to convince her of anything, but I think it will go a lot smoother for you (and her) if you do what you can to keep her involved.
Next time she wants to go to a fast food restaurant, maybe suggest going to a different place? "Hey mom, do you think we could go to "X" instead? I hear they have some really great food that's much healthier for us" Maybe if she's more involved she'll be able to back off a bit.
In any case, hang in there!