I actually am feeling more pressure about this now that my kids are older. My parents (who live literally across the country from us) were not going to advocate "alone time" with infants/toddlers that would involve them flying that far. Now that the kids are older (only 8,7, and 7, mind) they are chomping at the bit for "when are you going to put them on a plane to come visit?" I couldn't believe that they were pushing that--while I did indeed hop planes by myself to spend a few weeks in the summer with my grandparents, it wasn't until I was 13!
I finally had to be pretty blunt, saying that I wouldn't even consider it until they were 12 AND ready, whichever came *later*. I did offer, since DH has never spent a lot of time on the east coast and we are history buffs, to dump the kids off for a week or two while DH and I did our own tour/sightseeing (not even staying at my parents house). That was rejected ("Oh, you wouldn't want to do that!") which instantly red flagged me. It could have been because they were disappointed with my answer.
I won't leave my kids alone overnight or longer with my parents until I know that at least one of the kids has the confidence and know how to pick up the phone and call me if there's a problem. My mom has had some pretty bad mental health issues, they don't like young children (or at least, don't seem to "get" it--at all, and they didn't during my childhood either). If my dad was around to help her manage her behavior, that would be one thing, but I know my dad and he'll just happily ignore things. So far I have not really wanted to open up THAT kind of honest can of worms. They do fine on visits/babysitting, esp. since early on we established boundaries and gave consistant and firm guidance.
I do expect this to blow up in my face when eventually they find out that MIL gets the kids overnight and may get them for a week this summer (MIL lives with SIL, so it'd be a cousin reunion too, and that house is set up for kids). Not that we have hidden it (and we won't) but we haven't proactively mentioned it either. But if it does, I think I will have the big honest sit down talk with them--and mom's likely nuclear crazy response to finding out will be a pretty big reason why I can't allow them to have the kids across the country from them. We'll see.
I do think it's normal for grandparents to want that--and healthy grandparents, not just disturbed ones. I think it can be good for the kids. I know my mom and grandma did not get along because of all the vicious stories/gossip my mom told when my grandma started suffering dementia, and that my grandparents were pretty harsh with my dad growing up--but they were great grandparents to me, and that place was my refuge from my hellish home life, and I never EVER saw taht side of them! So I get it. Sometimes it makes me sad and angry that I have to be so paranoid. But...oh well, that's part of what sucks about negotiating being both a parent (to your kid) simultaneously with being a kid (to your parents) and getting all mixed up in that protective/craving approval thing.