I fear that taking special time with family away only sends the message, "If you are misbehaving, you are not loveable." Punishments should never, ever include restricting love (which equals TIME).
You could possibly restrict what she is allowed to do during said vist, perhaps tell her "You will not be able to go to the movies with Grandma because you have misbehaved" instead.
I personally wouldn't have punished my kid for writing her name on her booster seat- if a child is left unsupervised with a writing utensil, I think the responsible party then becomes the person who left them unsupervised with said utensil! (I have a seven-year-old- Newton's law applies 100% of the time!) I would have only said, it is not acceptable to write on items or furniture unless I have given you permission.
I think that it's important to find her currency and use it to your advantage and her benefit. My daughter is finally interested in money so now we are making her pay quarters every time she disrespects someone or behaves badly. Boy, does that work! She earns commission when she does her chores, does good deeds, acts of kindness, etc.
Good luck!