It is possible that your stepdaughter is not dependent and helpless, but afraid of getting into trouble or being scolded. Children are often exposed to a lot of fighting when their parents divorce and they can become emotionally constricted. This is one possibility.
I certainly would not try to compete with the entertainment her mother provides-–it's not necessary, and it won't help. Instead, offer your time to your stepdaughter and do fun things with her such as biking together or playing games or coloring. And then explain to her that you have things to do and it's time for her to make her own fun. Does your stepdaughter have any playthings at your home? Does she have her own room? It is important for children whose parents are divorced to feel they have two homes: there is mom's house and there is dad's house. I also strongly recommend that her father find ways to spend one-on-one time with his child. I see many dads who do not recognize that their children miss them and expect their new wife to spend most of their time with his child. Another suggestion is to try a behavior chart, which can help inspire children to change their behavior. First, explain to your stepdaughter what is special about her; compliment and praise her. Then, point out now that she is 7, she needs to find more ways to entertain herself when she feels bored. Explain that you want to help her become more grown up and how you will set up a big girl chart on the refrigerator. Whenever she finds fun things to do on her own, she will earn a star. A lot of stars can be traded in for a privilege such as making popcorn, renting a favorite video or playing a special game with dad.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.