It sounds like you have a very specific view of how grandparents 'should' act. I think that's actually how many people think grandparents act, but they aren't all like that. Some grandparents just aren't into babies. Some aren't into kids of any age. Some have other priorities. Some are too old or sick or worn out from a rough life to be able to give their all to a little tiny helpless person. And if your mom is depressed, only getting 2 hours of sleep a night, etc. I really don't expect her to even change out of her pj's, nevermind come over & babysit! And as someone with a chronic illness, I can understand why she might be too tired to even take a walk in the driveway.
My own parents aren't currently a part of our lives but my mom was similar to yours in that she didn't interact with DS. I guess she wanted to see him but didn't want any of the work involved in engaging or playing with him. She straight up told me that she would never be able to watch DS while I work like other grandparents she knows do for their grandkids. She just isn't very high-energy, she wants to watch TV and stuff. Neither of my parents are allowed to see DS right now though, for unrelated reasons. DH's parents invite us over and claim to be eager to see DS but when we're there, they hang out in the other room drinking while I play with DS. I'll be honest, I don't always see the point in visiting, I can play with DS at home lol, but we do it anyway because at least he will sort of know one set of grandparents. None of DS's four grandparents have ever babysat him. Not all grandparents can be the warm, cuddly, tell you stories & bake cookies type! I'm so sorry, though, that she is not able to be the grandmother you want for your DD.