I think your parents are like the stereotypical grandparents, spoiling the child. Which is OK if the grandparents only visit once in a while. But if they are constantly at your house, then you have to impose rules and they need to stick to them.

It's a sign that your parents don't respect boundaries that, even after you tell them how to treat YOUR dog, they don't go along. Now, you might be a little too draconian - sitting on the floor with your dog or occasionally giving her too many treats is not the end of the world. But since they are ALWAYS undercutting you, this is a real issue.

Not only that, it's not good for the dog. When she's an adult, it will not be nearly as cute when she jumps on people, and begging at the table can get old real fast. Maybe explain that to them?