C.B.
I'd have her give real good reasons why she's wanting to stay home and play. Something just doesn't sound right. If you sign her up for something, I wouldn't let her wimp out. Follow through is something she needs to learn too. But it sounds like some type of fear that's behind it. But cut back on how many extra things to get her involved in. Parents often overdo it with signing the kids up for this AND that. Maybe just one extra class besides school would be enough.
I think 6 year olds can find plenty to be scared of. But there's always time to play at home, after scouts, after swim, after dance, after school. Life isn't going to end by going to her other places.