It seems to me that your sister is the one being unreasonable. Unless you made some kind of commitment to act as a primary care-taker of her child, you have the same right to make choices about how to live your life as she does. Your personal goals – which right now likely include growing a career and having an active social life – are no less relevant than hers. Pursuing them doesn’t make you selfish.
Then again, a wonderful thing about family (ideally) is being a part of a caring and reliable support system. I encourage moms to reach out to extended family members for help when they feel exhausted or overwhelmed by their child-rearing responsibilities. Your sister may be turning to you because she fully trusts you with her child and feels more secure with her daughter in your care than anyone else’s. This is a compliment to you.
You also have an opportunity to be a special and influential part of your niece’s life – you’re another strong female role model for her. If your sister is a stay-at-home mom, you will show your niece another equally viable lifestyle choice women have.
Still, your sister needs to respect you and support your personal life. She needs to know you won’t always be able to accommodate her schedule.
If your sister continues to become angry and resentful, her feelings may be rooted in something deeper. Some people make a direct connection between what people give them or do for them and how much they feel they are loved and valued by those people. Your sister, for example, might take a “no” to babysitting from you not as a missed opportunity to go to the mall, but as a sign that you don’t love her enough to help out. If she seems to always be evaluating your relationship in terms of “what have you done for me lately,” then it may be that low self-esteem keeps her constantly looking for tangible “proof” that you really love her.
If you suspect this may be the case, try to head off her tendency to think this way by offering some reassurance next time you decline her request (“I’m busy this Friday night, but I really do want to see Susie soon”).
Another idea, which allows you to spend time with your niece when it’s convenient for you and give your sister a break, is to take a look at your schedule and pre-arrange the visits. This way, your sister can plan her non-emergency outings without her daughter around your visits without even having to ask for your time, and you won’t feel put on the spot when you have to say no. Everybody (especially your niece) wins.