C.L.
If she thinks she should be paid for working, then PAY HER! You say she is constantly nagging you, so PAY HER! Why should she HAVE to nag you? You say you don't know what to do....SURE you do, PAY HER!
How can she get this through YOUR head, she wants to be PAID! You have to give her credit, she is doing her best to communicate with you. You just don't like what she's saying.
Sit down with her and apologize to her thinking only of yourself and for not taking her feelings into consideration. Ask her how much she wants to be paid. If it's less than $100 per week, consider yourself lucky. If it's MORE than what you can get elsewhere, go with another provider. Nowhere in her "grandmother's handbook" does it say she is obliged to provide full time care (for FREE no less) for her daughter's child.
If you continue your current route, there is a good chance your mother won't want to spend ANY time with you or your daugther. Don't squander her good graces.
Do this today. In fact, bring her a handful of wildflowers when you pick up your daughter this afternoon.
Good luck, you can do this.