I think you are a WONDERFUL mother (I know you are step-mom, but you are mothering wonderfully!)
My dd has a friend who sounds a lot like your SD. My dd is (not through my doing, she jus was born to be) a very quiet, polite, docile, obedient child. Since she was an only child for nearly 5 years, she's also sensitive to noise and energy in her environment. She's used to a very calm house.
She has a classmate who is a wonderful person, but high energy, bossy, rude and often brings a lot of negativity with her in the way she speaks and processes experiences. (She also has a lot of wonderful qualities) My dd will occasionally have a playdate with her when it is suggested over and over again, but most of the time she asks not to.
I have really felt for this child. She just has a lot of growing to do in order to be accepted into social situations. She's not a bad person, she's really reallly sweet and she's a child. No adult is perfect, much less a child. They're learning. Still, it's hard to push it on to my dd, as I want to respect her boundaries, too.
If I were you I would approace a mom you know and would like your child to play with. Explain to her your situation and lay it all out, good and bad. Tell her that your dd is heartbroken and you're wondering if that mom might be able to help her learn manners and social skills in a playdate. I think moms would be more receptive if you frame it like that than if you just drop her off at someone's house and they see a child who is kind of rude.
It's not easy and I feel for both of you. I wish you all the best.