When in Grandma or Pop-Pop's care, do they tend to poo-poo junior's bad actions or, on the flip side, take on an aggressive discipline approach? This is a tough topic to broach with grandparents. For the grandparents who laugh off your kiddo's bad choices, keep in mind that they may simply feel uncomfortable laying down the law with your child because they're not his or her parents. They want to be the good guys and be loved by your kid.
What to Do:
If Gran and Gramps can't lay down the law when caring for your kids, ask them to simply give the warning that all consequences will be given out upon your or the other parent's return, that way kids know a consequence is coming and will be delivered, but Gran and Gramps are free of being the bad guy.
If you can convince the grandparents to lay down the law, it would be better. Perhaps ask them to stick to short-term consequences such as time-outs — and then in situations when your kid really acts out, allow them to warn that a further consequence will be handed out upon your return.
The overly-aggressive grandparent may simply be the mark of personality or generation. Our generation is not resorting to spanking the way my parents' generation did. You may find that your child's grandparent resorts to yelling or threats of spanking when caring for your kid. This is not an appropriate action by a grandparent (or any parent in my opinion), although . . . we all yell sometimes.
You're going to have to be the tough guy and tell the grandparents that there is to be no spanking, no threats of spanking, and no yelling allowed (although a yell here and there is acceptably human). State that you understand how sometimes people yell — it happens — but that you would like them to try to control or modify the amount of yelling and especially the words they're using in regards to discipline. Be sure to emphasize that hitting, spanking, or threats of either are not acceptable, and if it continues you may not allow them to babysit or have alone time anymore.
The fact is that these methods of discipline may seem innocent or appropriate or not harmful to them because that's what they were raised with. Keep this in mind when approaching them and explain that while you understand that they turned out beautiful and great kids, that you and your partner are trying a different approach in parenting with your kids, and you hope they will respect your wishes.
Respectfully address them. Acknowledge generational differences. Keep communication open.