OK, sounds like to your daughter this has become a power/control issue. Since I assume you must drive places occasionally and it is definitely not an option for her to not be in the seat when you do, I recommend you take a hard line on this one. You need to take back control of this situation.
So, on a day or two where you don't *have* to go anywhere (doctor/stores/errands), you talk up a trip to the park, or a playgroup or something else that is fun for her but not required that you go to. Explain before you go to get in the car that she needs to sit nicely in her seat as quick as she can (make a game out of it, some reverse psychology works well) to be buckled in and no screaming or fussing or you will not take her. Period.
Then you must consistently follow up on it. Set the standard you want to live with - so if you want her in her seat right away hold her to that, do not allow her to play for ten minutes (much less 30!) Put her directly in the carseat (or allow her to climb in herself if she can), if she screams give her one warning, then take her out of the car, telling her that it's too bad you can't go to the pool/park/etc. Wait a couple of hours and try again. She's old enough to understand consequences, so make sure not to reward her for misbehaving when you go back into the house, either.
Besides the stick, you can also use the carrot approach. Make a chart, give her a sticker whenever she does something right (without fussing), this can include riding in the car. Or you can make one up just for the car. If she gets X number of stickers, then she can pick out a toy/treat/trip to the park.
Making it a game (how fast can she the two of you get her buckled in, singing a funny song, making faces to get her to laugh, making it tickle, etc.) is helpful and you can do that every time as you are buckling her in, but when it comes down to it, put her in the seat right away and buckle her in, regardless of her temper tantrums. The bigger she gets, the harder it will be to do, so you need to establish this *now*.
Please don't "feel terrible" about her screaming. She's angry and using that noise to express herself and to manipulate you, if you let her. So, don't let her. If you don't react, she will get bored of it. Get earplugs. When it all boils down to it, sometimes we *all* have to do things we don't like or want to do and children are no exception (taking medicine/visiting the doctor or dentist, etc.)
The trick is always figuring out which stick and/or carrot to be using in each situation. If you can resolve this well now, you will go a long way towards minimizing future power/control battles with her. (And trust me, there will be many!)
Good luck!