Hi there, I get your frustration and boy, have I been there ...not necessarily with shoes but other things along the road ...even into teenage hood I have to tell you. You have had enough input from other people obviously - so please ignore this if not helpful. One good thing about input is that if it doesn't fit with you , it is still helping you affirm what does sit right with you. My suggestion would be to approach it from a number of angles...
*make keeping her shoes on more fun than throwing them around (make up a song about it, ,we had a song called "do you put your ...(hat).... on your ...(ears...) ?" ....leading up to, "No , we put our (hat) on our head" , or maybe you could make a game of how long can she keep the on )
*if it's realistic change the goal and focus from not throwing shoes around to having shoes on by the time you stop the car. Whatever your goal, have loads of positive reinforcement for it, explain how it helps you and how much you appreciate it
* consider some special shoes that are not for throwing around the car (that she can put on herself). Maybe she doesn't get to wear them unless they stay on her feet or whatever...
*make time in the car really fun with shoes on (or not thrown)
*can you work out what drives her to do this throwing etc? can you provide another/apropriate outlet fro this either in the car or at another time?
*take the emphasis off solely shoes eg are you ready when we stop - shoes, hat, etc, - does doll have shoes and hat on too? It's an exciting stage to be able to get shoes off - make it fun at home and encourage the putting on of clothing too- you might need to be prepared to go out with odd socks etc...
*reward small steps towards the goal , be really encouraging of her efforts
*be patient with her and yourself - it takes us all a while to change patterns
*have a strategy if it doesn't go to plan. If you're sitting in the car and it's snowing and one shoe is in the trunk and you can't find the other, and you're late from something, and you're worrying how on earth will I cope with this when I have three children.... try to look at it from another plane, take a deep breath and see the funny side of it if possible. I have a friend who chooses particular songs to sing/hum to herself at times like that.
*Allow yourself to take the time you need to support your child (and yourself) in this. Don't worry about being late -your relationship with your child is more important and how you deal with these day to day issues is what lasts and contributes to defining your relationship.
*As a mother a long way down the road, I would say be kind to yourself wherever you can (we say 'chill out' in NZ) . In a few years you'll look back and laugh as your remember how stressful these moments were (and there will be plenty more) , but you'll have a different perspective. In my experience each successive child has given me an exponential challenge in 'letting go". All the best for your journey. Well Done for recognising this hotspot and seeking gentle discipline.