Dear sdp,
You're a kind and generous person. However, it's not your daughter and you're not responsible for her. Let mom take care of her since she's getting the child support.
I know this is hard to do because we all melt when it comes to kids, but your sil is really taking advantage and she knows her silly sil will watch W when she wants to have her good time.
If she's not a fit mother and she's shoving the girl off on everyone else, maybe it's time for someone to report her. She's getting support and she's got to justify every cent and prove how it's being used for the girls benefit. Also, if sil is leaving the girl home by herself, social services would be very interested in learning about that.
Like you said, kick back and spend that time with your own family. Your plate is full enough. You don't need to take on anymore.
Blessings, Kathy