The situation has drastically changed with the addition of stepchildren whose behavior is unmanageable. It's unreasonable to expect someone to voluntarily take on the burden of caring for children that even their own grandparents avoid. The request is excessive, and it's understandable that OP would want to protect her own children and maintain a peaceful home environment.
OP's refusal stems from a clear bias against her sister's stepchildren. While bad behavior is a factor, the underlying issue is a lack of willingness to accept these children as part of the family. OP is prioritizing convenience and personal comfort over familial support and integration, revealing a selfish motive cloaked in concerns about behavior.
The core issue revolves around the extension of a previously agreed-upon childcare arrangement to include stepchildren with behavioral issues. While the stepchildren's behavior is a legitimate concern, the family dynamic and potential resentment among the children are also factors. OP is not obligated to provide childcare, especially under significantly altered circumstances. However, a more empathetic approach could have mitigated the hurt feelings.