D.K.
Hi J.,
We have a similar situation at my house. My MIL's golden children are my husband's first son (from his first marriage) and my SIL's son. My first son (from my first marriage) and my husband's and my little 15mo boy are the children that get overlooked. I just don't know what to make of this except it seems like she just doesn't like being around my kids because I don't let her take over and boss me around about them like my SIL does and like my hub's ex-wife used to. She has even tried to take us to task in front of the children for the way we discipline my step-son when he's with us over the summer. Of course we weren't having any of it, but the fact remains that she's uncomfortable with children that she can't personally control.
As for what you should do, just do what we do. We just leave everything up to her. We don't invite her to come for visits or anything any more, we just let her handle it. If she wants to come, she'll call etc.. As a grandmother, she should WANT a relationship with your children, and if she doesn't that's her problem. She is a grown woman and you shouldn't have to waste time and experience stress trying to get her to behave as a grandmother. Mothering her is not your job, mothering your own child is. As long as your child has plenty of loving people in his life that he knows he can look up to, I would say that he'll be just fine. He may even grown up to prefer the way he was rasied without a poisonous influence like a grandmother that obviously plays favorites.
Maybe just write her a quick e-mail or a note. Something non-confrontational like "Since we seem to come up against a lot of scheduling conflicts (or whatever her excuses are), I was thinking that maybe it would be a better idea if you just let us know when you're available to spend some time with the kids if you wish. That way we can make sure to schedule around it." That drops the ball firmly in her lap and if she chooses to not ever call and ask to see them, then you have your answer. You ONLY want people around your kids that will love and cherish them.
Best of luck, and don't let it get to you...some people just don't have hearts big enough for all of the people in their lives that need their love.