Well to me it would depend on the circumstances. Is there a reason the other grandmother can't come to you? Is it very inconvenient to go to the other grandmothers home to pick up whatever it is? If you are being asked to go out of your way to accommodate someone who really doesn't give a darn, then I can 100% understand your hesitance to do it. But, if it's not a difficult task, I say you suck it up... be the bigger person and do it. By going will it harm your grand child in any way? Most likely it may make her feel a litter better to see her grandmother for a little while. But by not going you're just causing more unnecessary tension and animosity between the families.
I'm in a similar situation with my in-laws, so I know where you're coming from. But sometimes for the sake of the child we just have to suck it up, put on a fake smile and deal w/these people.