All your parents want is the love of your children, and their respect. It is easy for children to back-answer grandparents. Teach them how to be respectful.
Grandparents, whose life revolves around their grandchildren, are rarely given the love they deserve or crave. On the other hand, those grandparents who have a life of their own, who are involved human beings, who have a social life, a career or fulfilling hobbies, tend to be more respected by their grandchildren.
Teach your children to be polite to their grandparents. This does not mean that you should quash every argument at the outset. Let the children and their grandparents speak their mind, but at the same time make sure that your children are not rude. If they back-answer once and get away with it, they will do so again, so you need to make sure that you check them the very first time they back-answer.
It makes more sense for the grandparent to check the child when the child is rude to him or her, or the child will feel that the grandparent is not able to stand up for himself or herself. Often parents drill it into the child's head that the adult is always right, and no matter, what, we should respect them. While certain respect is due to every elderly person, there is only so much respect a child will give. After that, a child will give respect where he feels respect is due, and no matter what you do, once your child grows up, if he feels an elderly person is not to be respected, the child will not hesitate before being short with such elderly person.
When you are sending your children to your grandparents home to spend the day, never give the children the feeling that they are doing their grandparents a favour by spending time with them. Let the children know that their grandparents love them and are happy to have them at any time, but the children should behave themselves when they are with their grandparents as neither the grandparents, nor you, will tolerate any nonsense.
You can allow your grandparents to spoil your children, but make sure your grandparents check the children if the children are ever rude to them.
Teach by example. Do not correct your parents in front of your children, as your children will tend to do the same. Similarly, never lose your temper with your parents, or raise your voice at them in front of your kids, even if it is for something like telling your parents to have their medication on time. Be as polite to your parents as possible in front of your children, and your children will follow your example.
While all parents know the effect their upbringing has on their children, they are still unable to pinpoint what they did right or wrong. When you go for a party with your children, do not come home and laugh about the antics of the guests with them, or speak bad about any particular aunt, uncle or relative. Your children will grow up to be negative, critical human beings, noticing the bad in someone before noticing the good. Instead, if you have a grouch with someone, discuss it with your spouse, not with your children. If you had an argument with someone, leave the kids out of it. Your children don't have to go out of their way to be nice to everyone, but showing respect and being civil to elders is the essence of good breeding.