ETA per your SWH - If none of this has helped, then you need to pull out the big guns. Make sure that she doesn't watch television or play with any electronics until she bends to your will on this. Put a calendar on the wall and mark with stickers each day that goes by that she obeys you. On days that she doesn't, mark a big FROWNY face. On days that she obeys, she can watch tv. When she pulls her arms out of the straps, take tv and any other fun activities off the table. Tell her that she doesn't get to have fun because of what she did in the car. If you were supposed to go somewhere fun later, THAT'S off the table too.
My son had temper tantrums for a while when he didn't get his way. He had a fit on the way to a matinee because he didn't want to stop for lunch first. Not only did we not go to the matinee, but we didn't go to lunch either. I drove right back home and put him in his room for an HOUR. I brought him a boring sandwich and gave it to him in his room and shut the door behind me. Everytime he cried to come out I told him that he made us miss movie and lunch out and he would stay in his room and think about his bad behavior until he learned that he could NOT treat his family this way.
This is what you need to do. Your child's behavior is more critical to fix than my child's was. Her life may depend on it.
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There are times you need to put the fear of God into a child. Running out in the street when a car is coming. Trying to touch a stove when the burner is hot. Stuff like that. THIS is one of these times.
Pull the car over and be HARSH with her. "You do NOT pull your arms out! NEVER!" If this doesn't work, then you need to take her most precious activity and toy away from her. If you go to gymnastics, for instance, take her and make her sit and WATCH her friends and NOT allow her to participate. If she has a favorite doll or lovey she sleeps with, take that too.
There should not have been a second time. You didn't discipline her enough if there was a second time. Don't let there be a third time.