The phrase that jumped out at me was very early on describing her "complex" relationship with her mother. I think that whilst op is beholden to her mother, and thinks she had equal say in her grandchildren's lives, she will never be free to make a sensible decision. Any parent who makes huge sacrifices for their children's education, decides to do that for themselves. They can't then expect the child to be eternally grateful, but that's what has happened her. Meanwhile, a generation later, I'm guessing her mother didn't have to deal with the current house prices, the traffic, or indeed the MS.
That her mother says the grandchild will change schools "over her dead body" is also very telling. Where do you think OP got her perspective/ behaviour from? She has much bigger issues with that relationship that needs acknowledging, and which are about to impact another generation of her family.
OPs mother has instilled her social and family requirements, but they do not work superimposed over the top of today's reality.
OP needs to worry more about what is ACTUALLY happening to her family, what is right in front of her, rather than trying to live up to the ideals and expectations of a previous lifetime.
Her daughter is never going to fit in. Either they live in a shed in an expensive area and she is perceived as an outsider, or she stays in a local school, and is raised to believe that she is better than everyone else, and believes herself to be an outsider.
A new child will come along, and in her eyes will be responsible for making her mother ill, and meanwhile she's being dragged to a school where she cannot naturally form afterschool activities and friendships.
Trust me, OP, your mother will not die because your daughter went to another school. She will, however, make your feel even worse about not continuing the facade that your family is somehow better, and entitled to a privileged life, that she had already sacrificed her life to prop up.