Well, she's the only grandchild now - perhaP's she doesn't want to create an expectation that she will do a day's unpaid childcare for each of her children.
I'd be interested to know exactly what was offered.
Saying you will help someone look after their child does not mean committing yourself to being an unpaid childminder while they work.
As self-employed people, childminders are often quite constrained in what holidays they can take, and certainly need to give plenty of notice to clients.
The upside of that rigidity is the fact that they earn their living that way.
Often people who mind their grandchildren are only "allowed" to take holidays when their "employer" (who pays them nothing for their time, despite profiting from it) takes theirs.
My retired MIL has struggled to come to visit us because she was being used in this way by her daughter. I'm sure her relationship with her own son was not the only one affected by being tied up in this way.
Grandparents can be of enormous help without exploiting them so you can keep more of your wages at their expense.
The offer of help could have been genuine without ever being meant as a promise to work for her daughter for free.
As for moving to be near her parents - sorry, but the OP us an adult, she makes her own choices about where she lives.
If she wants to be near her parents to avail of the (enormous) benefits of having family nearby, that is up to her. It doesn't entitle her to free childcare.
The very idea of leaving a man recovering from cancer in sole charge of a toddler one day a week is appalling.
Parents deserve better than that.