A couple of things from me. My brother used to be like your daughter. We never found out why, only that it did at some point stop and from around the age of 4 he suddenly became fine with the car, so for your sake I hope your daughter goes that route. Me, on the other hand? I’ve had car sickness my entire life and cannot sit in the back of a car for longer than a few minutes without it being an issue.
It could be that your daughter gets motion sickness, so I would try the travel wrist bands and see if that helps. But also, if she is feeling unwell on public transport as well as in cars - which would make sense if she feels sick there - it will take her a while to unlearn the fact that travelling makes her feel ill and that she gets stressed in anticipation of the horrible thing happening, which of course makes it almost inevitable.
I don’t know how you’re set up with technology, but in the accessibility setting for iPhones and iPads there is a motion sickness option that puts dots on the screen and uses the accelerometer in the device to guide their movement on the screen and apparently helps a lot because it provides an artificial horizon of sorts for people to look at. I’ve not had a chance to use it myself and test how well it works, because I mostly drive myself, but I’ve heard good things from friends. So maybe if that’s an option, give her a chance to try it and see how that goes.
Also, cars, public transport, all of those things, are noisy environments. Have you tried putting ear defenders on your daughter to see whether that helps her? Something in the environment is causing her distress, so what you need is to try to work out what that is.
To pick up on what another poster said about migraine, my son and I both get migraines and he used to scream the car down if we ever dropped below 30mph. I first worked out he had migraines when he was about 7 and a loud noise made him puke, because that was very familiar to me. Adults with migraine often start as children with abdominal migraines, because of all the neural tissue in the gut, and so it is possible that this is a factor but she’s too small to be able to communicate what she’s feeling.
While this all feels quite hard to solve right now, there is no harm in talking to her GP about this and about what you may be able to do to support her either with car sickness or possible early migraine signs. My father was of the “she’ll have to get used to it” school of thought and every childhood road trip was a misery to me as a result. I did my best to make sure I didn’t repeat that with my son because a childhood full of “stop being so dramatic” never actually fixed anything. Quite the reverse.
But first step: talk to the GP. If nothing else, being able to tell the grandparents that the doctor has suggested X, Y or Z and so you’re going to have to stick to that while you work out the cause may actually make them more inclined to be understanding.