Sometimes it's the other way around: your parents are a dream, but your stepkids are impossible! If the kids are being overly chilly to your parents, the kids might not realize that it's okay not to love them. They may have picked up a complaint against them from you or your partner (watch your tongue, now!), or they may be worried about betraying their own grandparents. So they pout and ignore.
Reassure the kids that they don't have to love or even like your parents. Increase familiarity by telling them a little about each parent. Seek shared interests or character traits. “You know how much you like magic? Well, Arthur, my dad, used to be a magician. He never tells his tricks, but if you asked him to help you learn to palm that ball, I bet he would.”
On the other hand, if your stepkids are being rude to your parents (or to their Grands or Other Grands), it's time for a talk. We all know kids can be cruel, and kids can be snooty. If it's not respectful, it's not acceptable. They need to know that.
Other Grands and You
The Other Grands are still a part of your stepchildren's family, and they always will be (even if the ex is deceased). You may never meet these people, they might act neutral, or they might be mean and try to poison your stepkids against you. You can try to resolve any problems, or you can let it slide, hoping, once again, that truth, justice, and the stepparent way will win out again. Whatever you do, remember that you can't divorce the children from their grandparents, even if your partner has no relationship with those grandparents anymore.
It may feel a little odd at first, inviting the parents of your partner's ex over, say, for dinner. There are no rules about what is right or wrong; go by your own comfort level. While you'll never feel comfortable hanging out with the ex's parents, people are pretty decent and will rise to the occasion in most cases.
Conflicts Between Grands, Other Grands, and Step-GrandsRivalry isn't just about siblings. Sometimes grandparents get competitive with each other, and because there are so many grandparents in a stepfamily situation, the squabbles can get quite extensive. I'm tempted to say that you should simply butt out and ignore them. They're all grown-ups. You don't, won't, and shouldn't have control over how these people are treating each other. But unfortunately, if there's a fight between them, you (and your mate, and way too often the stepkids) are the ones who are going to be caught in the cross-fire.
Steer clear! Avoid taking sides. If it gets too horrendous, then the solution is to call a therapist for yourself and maybe for the kids. Talk with the kids to make sure they're hanging in there. Assure them that you care about them.
Separation Is a Last Resort
Grandparents are so important to kids, and kids are so important to grandparents that it's imperative to try to work out any and all problems. A lot of the burden here is on you; you need to be explicit about what kind of behavior is needed from everyone involved.
Grandparents may be a bad influence on the kids, they may say nasty things about you and your family, and they may have different beliefs and try to impose those on the children. Take a leap of faith—you have tremendous influence on your stepkids. That influence may be challenged, but it's not threatened, by the grandparents. The world is full of people who have other things, both good and bad, to offer. All you can do is teach kids your own values the best you can and then let them go.