Your parent's and your partners parents may feel a sense of entitlement in how they handle your children, their grandchildren. They assert authority over you, your partner and your children. Often they assume theses methods must have worked for you or your partner, hence the methods in question should therefore be repeated to the next generation.
We'll all heard the saying, from our parents that their grandchildren will be their revenge. This is often said in good natured humor, but often it's a self profiling prophecy. The saying is a curse, directed at you by the grandparents, that negatively effective each generation, including the generation enacting the vengeance. It's a cycle, of generations cursing one another, far worse than even the infamous F-word. It's encouraging conflicts between parents and their children and grandma and grandpa often cause many of the conflicts. Grandparents will often undermine the authority of the parent, which can lead to emotional and behavior problems in the children involved.
One method that has given me success is explaining to my parents that their methods, though well intended, was actually harmful. For example my mother took my toddler daughter to a park, where they encountered a preschool aged little girl. My daughter referred to the little girl as a boy. This naturally upset the other girl, when my daughter kept calling her a boy, even after the little girl corrected her.
My mother saw this as cute and amusing. She was telling me about what happened and expected me to be equally amused. I was not. I reminded my mom that she had encouraged this behavior in myself when I was my daughter's age. I explained to her, even though it seemed funny, to the little girl being teased it was abuse.That this was teaching my daughter to be a bully and could cause social delay, which I myself suffered.
Explaining the consequences of the parenting action is often effective. However your child's grandparents may not be willing to listen to reason and you may be forced to constantly supervised them, restrict access to your children or if necessary even cut them off. Though please leave the latter for a last resort.
Sometimes it's better to tough it out, until their method bites them in the ass. Allowing your children to show them the errors of their ways. For example if someone gives your child sugar, make them deal with the hyper active little speed demon, as a consequence of their own stupidity
Usually when grandparents and other families behave in this matter, is a reaction to the changes happening in their life. Empty nest, loss of a spouse, a move, loneliness, depression, etc... while your life is speeding up with a family, a relationship, work, school, and whatever is on your plate, these trouble makers in your life could be crying for help, as the dinner table for them becomes smaller.
It sometimes helps to be the bigger person and react with sympathy and kindness.