First, I would change your "A little about me" to "Mom to two beautiful boys and a beautiful step-daughter..."
She is probably upset because she is just a visitor. I would figure out as many ways as possible for you to spend one-on-one time with her (Saturday breakfast or lunch or movie or shopping, you get the idea). Then more importantly, encourage your husband to spend one-on-one dates with her. He should actually treat it like a date so she learns how to be treated when she starts dating (hopefully a long time from now). Your two boys get their day full-time but she only gets him part-time. She doesn't want to share him during those precious few times.
On one of your lunches, tell your step-daughter that you just read about how much better it is for kids to be told what they can do and not "no, don't..." Ask her if she would like to help you try it. Instead of saying "Don't write on the walls!", say "Here, write on this paper." You get the idea.
Then ask her what kinds of things she likes to do. Are there some things she would like to cook or bake? Would she like to get some crafts? These are things she can do and not feel like she has to hang out with her little brothers.
You could also tell her that you think she should get an allowance for helping around the house. Ask her what she is good at. Then suggest more things. Does she like organizing things (closets, drawers)? Does she prefer to wash dishes or put them away? Would she rather vacuum or sweep the tile floor? Is she good at laundry? Then tell her some things you could do as a reward for her help - Shopping for school clothes, etc.
When she sees that she is loved, appreciated, and has roles in the family, she will enjoy herself more and not feel like such an outsider. Yes, it seems like a burden to have to go through so much trouble, but she is stuck with a split life and probably doesn't like it either. I hope you develop a great relationship with her. It will be so much better when she is older and your husband will love you more.