Grandma isn't obligated to do shit for a child that's not related to her. My grandmother didn't have to do half the shit she did for my brothers, but she did. I mean I got more than them, every time she got me something. My brothers weren't getting something. This situation was basically my granny accepting my two younger brothers.
Now as far as me, I was the child from a previous marriage. My stepdads family accepted me, I was like 2-3. When my two brothers came along, of course their grandmother went over and beyond for them and somethings I wasn't included in. I was cool though.
Grandma is not responsible for picking up on shit that the others parent or grandparents are lacking in. Would it be thoughtful, yes but she ain't gotta do a damn thing for that child.
So to say a grandma isn't obligated to do for either of the kids is a stretch because if granny ain't obligated to do for her own blood, she for damn sure ain't obligated to do shit for a mf who ain't no kin to her.