I thought you needed to wash the carriage? That was a bit obscure for me as a kid.
I replayed the remastered game a couple of years ago on PS4 with my daughter who was seven years old, and this time the only thing I was stuck on was the cat puzzle with the squeaky mattresses. I read a blog post just now about that puzzle, and it's special because you use the Use verb on two different things outside of your inventory. You usually go inventory->world or inventory->inventory, but here it's world->world. So I had to look up that one solution in the whole game.
Playing as an adult, it's much easier to keep in mind what clues you have and what the open puzzles are. As a kid, I would just start using everything with everything else, and the hints from failed interactions wouldn't clue me in. Now I see they make a really god job at telling you why things don't work and what you should try instead.
I was pleasantly surprised that my daughter thought the game was hilarious. I expected her to get bored quickly, but we played through it all together.