If, OP, you Mum agreed to do every monday (for example), she has signed herself up to every monday. For the foreseeable future. No events with her friends, no sporadic long weekends away, and what if she wants to go abroad for a week, fortnight or month? Maybe she is regretting saying yes, and by asking for payment she is giving you the option to put DD in nursery for an extra day.
Ad Hoc care from the GPs is nice, and imo something they should want to do every now and again, not all the time, and for free (because they specifically want to spend that day with their DC). However, arranged, formal care should be paid for.
I do think she is BU for asking for the same rate as the Nursery, as they are paid on reflection of overheads, staffing, qualifications, of which she mas minimal. I think it would have been nice if, when asking her to do a certain day you offered to contribute, as she may actually be asking as she thinks it would have been more polite for you to offer and her decline.
Fwiw, my Dmum will be providing childcare for me when I return to work, however she is a Childminder, and I have insisted that, as she will be giving up a place for another child in order to have mine, that I pay her her going rate. She has agreed, but under duress, as she thinks she should be able to provide help as and when I need it for free. I, on the other hand, do not want to take advantage of her good nature.