The parents know that their kids are telling the truth and actually going with The Cat in the Hat and they don't mind.
- After all, they always come back home safely, the Cat makes sure that they buckle up, and they learn some neat stuff.
- For what it's worth, the 1970s animated special ended with the kids' mother telling them that she met the Cat in the Hat on his way out.
- And he was carrying a moss-covered three-handled family gradunza, to boot.
- It's also worth noting that as soon as they get permission in this series, they immediately and with no loss of volume yell to the Cat "We can go! We can go!" and he ecstatically bellows back "I know, I know!!" Neither of the moms is deaf, so they're either in on it, in deep denial or we're supposed to assume some sort of only-the-children-can-hear-him situation... which doesn't really explain why they're also apparently ignoring the literal brass band parade that is the Thingamajigger taking off.
The Thingamajigger was developed in the same factory (Or by the same person) where The Magic School Bus was createdBoth have weird elaborate buttons that can do literally anything, both can shrink, can turn into a submarine etc...