Ahh.. fellow sufferers. I posted some messages on this a while back and got lots of useful advice from mumsnet people. See 'doping your baby' and 'baby houdini' boards if you're interested.
I have a major, major, wriggling problem with my toddler. My oldest didn't exhibit this behavior early on, but he made up for it later with in-car tantrums so very similar to the ones you describe, Gaby.
It's a wonder older son and I aren't covered in battle scars. We certainly ended up having near-fisticuffs at times.
I can't offer any failsafe solution, only tons of sympathy. This sort of situation can make you into the sort of parent - and person - you don't want to be. My son, now aged 7, has grown out of it. Hardly a murmer, though I have to make a point of asking him if he has his seat belt on mid-journey. He has a worrying habit of taking it off, thinking it's 'cool' to travel unrestricted. Anyway I'm rambling...
For what it's worth, here are the things I did when he was 4 - 5 ish. None worked 100%, but they made life a little easier. You say you've tried all the usual things - same here. I tended to settle for a very matter of fact voice, firm manner and tried very hard to resist being drawn into long verbal arguments, fighting on their level. Not easy, though. Bearing that in mind here goes:
Prepare the way. Hopefully this will ease your daughter into the idea of a car journey. Say 'we're going in the car in 10 minutes, so choose a toy to take with you (or something nice to eat or drink)' Then put the chosen item into your handbag. When you get to the car tell her she can have the item only when she is strapped in nicely. Stay firm on this. This tactic works well with my son, especially with food and drink.
If she still tantrums, or you don't want to try the handbag idea, what about this? Very matter-of-factly, and without looking at her for a reaction, begin to take her out of the car. Tell her she's going back home while you go out now and say good bye to her. Ideally, for authenticity this line has to be taken when there's an adult in the house you are leaving. However in desperation I used to go into 'strange mad mum mode' and tell my son I simply had to go out now, and if he wasn't coming with me that was absolutley fine but would he mind being along for the morning? Then say an airy 'good bye'. The 'good bye' bit seemed to be the trigger for a reversal of behavour. This tactic did work very well, though what the neightbours thought I cannot imagine.
You could try sweet reason. Say that if you go right now, you will have time to go to the shops AND the playground. Any delay and you'll have to give the playground a miss. This tended to make my son even angrier, though.
Lastly, and leading on from the above, 'counting
to five' for a bit of cooperation with some bribery thrown in for good measure. As in " If we go right now, we can see a video when we go home. No sitting, no video. Now I'm going to count to 5 and I want you sitting in your seat". Strangely while reason was ignored , 'counting to five' was pretty successful.
The very best of luck.