A.,
I can identify with your situation, but my family has a slightly different twist. My partner's parents live across the country. We see them once every three years or so. They like for us to visit for a week at a time, but NEVER offered to watch our son so we could go out alone, or even take a nap. NEVER. My dad and his wife life in central Oregon and claim they are "just sick" over not seeing our son, but never come to visit. (My sisters and their sons live in the same town, so I imagine they are getting their grandson fix met!:)) and my own mother is so toxic that all of my siblings and I had to cut her off from seeing any of us.
So, we are kind of in the same boat; no real grandparents around to watch our children grow up.
It's kind of sad, but we have accepted that these are THEIR choices, not ours, and we can't control other people. What we have decided to do is to foster the best POSSIBLE relationships between each of the functioning sets of grandparents and our son. That means, on our end, sending photos and being available when their interest arises. I send my in-laws pictures and cards every few months or so with updates of how our their grandson is growing. We have figured out that they will be wonderful grandparents via the postal service and they will do their best to engage him with we visit. (Little kids are messy and loud, which is not their cup of tea. Distance works better.) My dad and his wife like to spend a little "alone" time playing with him when we get together, but not too much, as little kids do tend to wear them out.
My advice to you would be to figure out how to capitalize on what each set of grandparents CAN offer. Would one set of them be be willing to take a trip with your family, staying in separate hotel rooms from the kids? Can you organize outings? As I've mentioned, my parents openly admit that kids just tire them out. Perhaps your sets of parents feel the same way, but are ashamed to admit it? (This requires admitting that we are getting older, not a pleasant thing to ponder for some of us!) Kids are exhausting at times. No matter what the reason, if the grandparents have dug their heels in about not wanting to watch the kids, respect it. Even if you don't agree with the reasons. And see if you can organize a trade with another family for child care.
One other thing that could be a pat answer is that when the kids ask to spend the night, just let them know that Grandpa and Grandma are "come visit" people, not "sleep-over party" people. It lets the kids know that it's not personal, and that different levels of engagement are acceptable. This is also a good answer to the questions that may arise about why "Timmy always spends the nights at his grandma's. Why don't I?" Making the grandparent's preference a part of their personality and not a response to your children will protect your kids from feeling rejected. And that's our most important job of all in a situation like this one.
My other suggestion is to find older people in your church who would appreciate the company of your kids. Maybe there's an older woman who wants to babysit? My own grandma was very much that type of person. Sometimes older men love to teach the younger ones a new craft, like building a birdhouse or a model. Thinking creatively about finding an older set of "Big Brother/Big Sister" types may foster your children having meaningful experiences with older folks who are open to the opportunity. These relationships can be very fulfilling for both parties, so I wouldn't hesitate to reach out and forge some new relationships in your community. Having your entire family engage in a caring and helpful relationship with older people can create your children will treasure in the years to come. Just make sure, in your heart, that what you are looking for is more than a babysitter. If not, then just pay for a babysitter. Be genuine in whatever you choose to do.
My best wishes to you and your family.