Would you pay this person?

Depends, do you want her grandmother to watch her? If you didn't ask her and she's telling you that she will be watching her for you and you will be paying her that's a more than a little pretentious and I would find a daycare where she can be around other kids and go on field trips and do fun activities. If you asked this person to watch your daughter and she said she will do it for payment, than that's your call. While it's a little strange for grandparents to insist on being paid to spend time with their own grandchildren- if you asked her to make a commitment for summer just because you umed it'd be free and easy childcare than you need to wake up to the real world where even grandparents need to make money.