Yeah you figured relationships out lol.

He's treating her like new mom after only dating for a year.

I really dont know where you got that from. You do realize that in order to progress in a relationship, you have to get closer, share more with each other and plan for the future at some point.
Would be pretty dumb to go from casually dating, her not knowing his daughter etc., to go straight into marriage with her suddenly taking a huge role in his life and that of his daughter, wouldnt it?

He doesn't get to have any influence on what car OP buys. Unless he wants to buy OP a car. Sure, he can have an opinion, but he has zero say.

Because he thinks this relationship is more serious than OP does and maybe even wants to plan for the future, because well, you have to at some point, he is an ass, right?

She can buy whatever she wants, but that this wasnt all that smart, that shouldnt be so hard to come by.
It shows a lack of consideration from OP at best and at worst she simply didnt care. Especially as he is a father of a young child, i have enough empathy left in me to see that this is at the very least something that could hurt him.

The people that say run and shit like that have lost their minds. *Only* dating for a year, some people marry in less than that, why would that make a difference lol.