My first thought about this situation that the parents want to hold their own private puppy bowl. I would still not allow the dog to go to their place without your supervision, OP.

"Sorry - no one shows off my dog but me."

Show her off? Is there something special about her (rare breed, Westminster dog show champion, etc.) or are they just overly doting 'grandparents'? Have there been other signs they favor her? Perhaps taping over OP's high school graduation with the pup's first birthday party or replacing his baby pictures with her puppy pictures.

To be fair, if you dog is more popular to your parents than you, then what does that say about you?

That's where you say "Where my dog goes I go. We're a package deal." If they won't agree to that then your dog doesn't go.

your life doesn't suck your dog is well loved

I'm really hoping you said no.

Now I really want to know what kind of dog you have. Is it some kind of interesting breed and/or is your dog just awesome? I know what it's like to have a dog everyone is interested in. He's a Standard Xoloitzcuintli and people fall in love with him everywhere we go. He's an incredible dog, both in looks and personality. My youngest brother made me promise that, if we ever make it back to our hometown where they still live, I have to bring him in for show and tell. If I charged $5 for a photo, I'd have made hundreds of dollars by now. He's a stellar example of the breed, but I think people would be intrigued even if he wasn't. It's not every day you see a 60 lb hairless dog.

Bring a keg. Then you will be able to stay! ??

Consider it a blessing in disguise when your parents guest list includes a dog and not you. Sounds like a bad or REALLY weird party.