Yeah, I think she's dreaming if she figures she won't have to pay extra for 11 or more hours a day. She's either bluffing (likely) or she is going to go with a dayhome that offers less quality care or changes the rates on her when they realize they are screwing themselves in the foot!!!
Either way; tough!! I know it's tempting (especially for us "people-pleasers") to adapt your rules and standards to fill a spot, but if you don't feel good or right about it DON'T DO IT!!!
PS- I don't know if this is full time or part time, but my part-time daily rate is higher than that, for my normal 10 hour day! I know it varies based on your area, but just thought I would let you know.