Another vicious MN thread where because there is so little oversight an OP gets a total kicking for asking for advice.
I am so sorry OP.
Yours is a very reasonable question.
I do not believe at all that grandparents should be asked for full-time childcare, but bloody hell, your children are not even allowed entry to their grandmothers house, talk about the other end of the scale!
I think it is awful behaviour from your mother and I really would be rethinking the relationship.
Absolutely no way I would tolerate such a double standard.
I wouldn't ask her again for help and likewise she would no longer be invited to visit us.
My children are grown up but I had several friends whose brothers children were the only welcome children in Granny's.
They spent huge time there and she simply had no interest nor time in seeing the other grandchildren.
One friend's brother's children got super involved in sport and suddenly they were busy on their weekends and travelling all over the place.
Then and only then, was she told to bring the children over. By this time, a full decade later they had their own lives, and the kids loved their other grandparents and had no interest.
Similarly with other friends, grandparents suddenly wondering why the now teenagers had zero interest in visiting and refused to because their grandparents suddenly had time and space for them.
None of my friends would entertain forcing their children to visit grandparents that had had zero interest in them for a decade.
It's surprisingly common for grandparents to favour one set of grandchildren.