If you decide to do it I would charge $50 for the night and $30 for the next day. So, it would cost $80.00. She may not take you up on this as it seems kind of steep to a mom. You need to charge enough so it's worth your while but not so much that it's outrageous.
I've done overnights for my daycare kids before. I charge $55.00 and my normal daily rate is $35.00 I couldn't do an overnight for any less. Even if they sleep wonderfully, I still don't sleep as well because I'm constantly aware that they're here.