Especially when you consider that something like a state law mandating car seats is only gonna exert upward pressure on the cost of a kid for people with higher incomes. Basically the poors are gonna pile into whatever vehicle they have and the law can fuck off. Nobody says "gee we shouldn't have another kid because we'll need X, Y and Z' (one of those being a bigger car in this case). That's just not how people make decisions at that level. If you want a kid you get a kid and you roll with it. You know it's gonna be expensive but you just deal.
Controlling for income is really really hard since basically everything about lifestyle has some relation to income. Controlling for income with sufficient accuracy that you can tease out an effect that itself correlates with income is gonna be neigh on impossible when you're looking for something that's a 2nd order effect. This is like trying to predict trout populations in Canada by chemically analyzing reindeer piss in Russia. You can do it but it's an exercise in measurement and it's gonna have zero practical utility since sooooo many other things will have affects that dwarf those of what you're measuring.
I think it's far more likely that rear seats have shrunk and car seats have grown because fertility rates have declined and regulators and manufacturers are therefore emboldened to do things that would be laughable in a world where three kid households were more common.