The house inspection is a formality, to make sure you don't have bizarre stuff in your house and aren't living in a slum I would tidy, but not freak out making everything spotless, they already know you have children. And don't worry about the car seats yet, they will provide them if necessary. We were always told that the child would come with the necessities, which would continue to follow the child to other homes as well.

Good luck, and let us know how you go!