Unfortunately, every time you stay or let her stay, she is learning "if I rebell enough I get my way". Your parents are hurting the situation, too, by calling you mean and wrong. She apparently gets what she wants at their house while she has rules at home. Yep, she likes their house better :) When your daughter is not around, let them know that they need to support you. From now on, do NOT give in. When you say it's time to go, it's time to go. You are the big person. When it's time to go don't say anything, go and put your things in the car so that your hands are empty. Empty hands are best when carrying a squirming child :) Go inside and let her know it's time to give hugs and say bye. As soon as she starts to act up, gently and firmly give her one warning to behave and give hugs. If she obeys react in a happy way and head out to the car. If not, pick her up immediately like you would normally carry her, have your parents kiss her, and leave. If your PARENTS start to act up as well, then tell them "Love you, see you tomorrow (or whenever)" in as cheerful voice you can manage, walk out the door and buckle her in the car. It may take many times to get everyone used to the new way of doing things, but is necessary. Putting her in time out at Gma & Gpa's just gets her extra time at their house and by the time you get home it's been too long between action and discipline for her age and will just seem mean to her. Just placing her in the car instead of a timeout is best.
Right now it's just at Grandma & Grandpa's house. The longer she uses tantrums as her way of getting what she wants the harder to break her of it later. She will start this at other places, too: McDonald's, friends' homes, at the store when she wants a candy or toy. None of us like being the "bad guy", but sometimes it is necessary. Just be constant and she will learn. Making her go home with you will NOT cut her relationship with her grandparents.