I have a step daughter from my DH first marriage and i say i never had such issues with her. It comes down to the individual child i think. You SD does sound incredibly clever though. I would off have admired that if the case was different. My SD is 9 and not even close to such behavior (smartwise that is). Yes, i think she hates the guts out of you and she is trying to make you pain....sad as it may sound. Control you and cause issues. I don't know what the doc said about her needing to control life through food, but i'd be more practical and just say that she wants to control you guys and get back at you for taking her dad away OR taking the chance that her dad MIGHT have had to go back with her mom. Sounds very commonplace but let it sink in, step children NEVER ever accept the fact that mom and dad will not be together again.......and some of them do wanna get back to the possible (in their minds) reason that mom and dad cannot be together again. In this case you are the problem and not her food savvy? And you should tell your husband to deal with her as appropriate. That is HIS place and not yours......as for you i'd say try talking to her honestly and be kind. If that doesn't work then simply fade away from the whole issue.........
take care
PS: Your DH should up himself and take care of the problem which is his daughter's behavior. His behavior is more unacceptable than your SD's in my book. Also when you SD said my mom won't allow me to call YOU mom, you should have said this "She is right, because i am not your mom. Your mom is only one. But i am one that cares deeply for you and is your friend if you let her" That would have shut her up believe me. In front of your whole family
The fact is i have said this to my own DSD.....without any comments from her. The result is that she said 'but you are a second mom to me' .........