Hi Hayley,
I wonder if yes, she is asserting herself about getting in the car, very possibly because she knows you want her to sleep, but I suspect it;s not all about sleep, but rather that it is wrapped up in her becoming more assertive (it's that age) in all things, and testing boundaries, does that make sense

So the car thing is just part of it. Like you say, she is the same with the coat, insisting you go back inside and wanting to make other decisions for herself, being very assertive, I remember it very well. IIWM even if you do hope she will sleep in the car I would try announcing beforehand, "We're going to 'wherever' in the car, you can have a little sleep if you want to, but you don't have to, it is up to you" and see if it makes a difference. Or you could try for total reverse psychology and tell her "Mammy doesn't want you to sleep in the car, so that you sleep well tonight"

I think I would try the first option first

Also try talking to her when you're having chill time, and just speak to her about everything, give her great detail about how important sleep is, ask her lots of questions about how she feels, what she prefers and name all of her emotions for her throughout the day, so she can help you understand more

Finger's crossed for a good night Hun.x.