I have a problem dealing with my step daughter and feel bad about the way I feel?

My husband is very close to her and I love that, but she is 21 and I find her repulsive. She is over weight, showers probably one a week so her hair is always greasy and hangs in her plate at the dinner table. She chews with her mouth open and talks when her mouth is full so food goes all over the place. She is constantly belching out loud and picking at her undies....She really creeps me out so badly that I have even gotten up from the dinner table and gotten sick from seeing her eat. He is always asking me to take her shopping with me or to work on some charity functions with me. I will take her shopping with me but I am frozen when it comes to taking her with me to other places..yes she belches in public also. Several times I have tried to talk with her about her social skill and presence and I haven't been mean - but every time it has come back to bite me in the form of a mean ex wife's wrath. This weekend I have a charity fashion show function that I have organized and he has offered her the opportunity to go with me. I honestly don't know what to do, I am so scared of this. Help please.