Sounds like Grandma (like all of us) has her limitations. Reaching out to you kids is one of them.
There is an old saying "A son's a son til he takes a wife but a daughter's a daughter all of you life". Her relationship with her daughter may be closer and it's easier for her esp since she seems to connect over sports.
What I wouldn't worry about is being seen as "pouting" if you don't go with H. You can make arrangements on your own to take the boys to see her, or go see her yourself. The ones that matter will "get it".
Who are you concerned about when you say you will be seen as pouting?
