I strongly disagree that my children's relationship with my in laws is only facilitated through me! My DH is not a cipher, he is a very involved parent and we make these kind of decisions together always.
My PILs I suspect would naturally tend to assume that any 'no' answers come from me, when actually that is not the case. It's probably just easier to imagine it's not your own child saying no to you.
We bend over backwards to facilitate a close relationship with both sets of GPs but overnight stays aren't necessary to a close bond. I was extremely close to my own GPs, neither set of whom ever looked after me overnight and in fact only very rarely looked after me without my parents present.
It is worth considering that children will often say to a Grandparent'yes' to please them and then tell their parents quietly later that they really don't want to.
Finally, there is no 'power balance' as someone mentioned earlier. My DH and I decide together what is best for our children.
We do try very hard to make sure everyone feels good about our decisions and avoid hurt. I love and respect my in laws and DPs and very much appreciate anything they do for us, but that doesn't mean they get to override our parenting decisions if they happen to disagree with them - neither set would dream of doing so btw.