The expression “biggest frog (toad) in the puddle” means: The person of most importance in any community or group.
The group or community is always a small one, otherwise the person would be a personage and “the biggest fish in the sea.”
Daddy is, usually, the biggest frog in a domestic puddle, especially if he wears the pants of the family, but in a small community the relatively important individual, and rarely does that importance spread beyond the community, may be the banker, the police chief, the preacher, or the boss politician.
He is, at any rate, the one to whom everyone kowtows. He’s the one making the loudest “kerchunk.”
We’ve had this Americanism for at least seventy-five years.