The King of Cartoons' Family is composed of the Queen and the baby Prince. They visited the Playhouse in the episode "Spring".
In the episode, when the King of Cartoons visits, he introduces his family - his wife the Queen and his brand-new son and heir, the Prince of Cartoons. The Flowers then introduce the arrival of the Queen of Cartoons (Myrna White) and the baby Prince of Cartoons, as they did to the King. Pee-wee, Cowboy Curtis, and the Playhouse denizens are amazed about how cute the Prince is as a baby. Pee-wee wonders where babies come from - he and some others make guesses like a stork bringing them, being placed on the doorstep of a house (being a foundling), or a being bought at the hospital like it's a store. Magic Screen shows everyone a film about it with the correct information.
Coincidentally, the secret word in this episode is "begin", which is featured in the King's cartoon introduction line: "Let the cartoon begin!"
Due to being an infant at the time, the Prince of Cartoons is uncredited in the cast, as it's unknown who played him.