Dealing with disappointment or with disappointing others is part of a normal, healthy adult life. It is also a fundamental part of having your own family. It is about balance. About doing favours for others but also about calling in favours. One one extreme of the spectrum you have leeches, on the other are the pushovers. Part of being an responsible adult is to not fall to these extremes and to not have contact with people who do.
Which brings us to OP and the sister. Judging from what OP wrote the sister is constantly forcing others to help her. She is constantly dropping their children off so that she has more time for herself. Which brings her close to leach territory. Because the thing is that you just can't ask for help all the time. Especially not when you yourself are at fault for the situation (she choses to have kids, she choses to be a single mom). At some point you have to be responsible yourself and have to manage some stuff on your own. Instead of taking your family hostage.