There is no secret family, unless if you mean the space family. Sometimes unstead of the matchmaker, you get the earthitchi tamagotchi. Then if you say YES, you will adamadically get the space family!
One is a male that has a leaf growing out of it's head and if you feed him sesame pudding he'll be a secret guy.
The other is a female that looks like a puff of cotton for a head and you give her the girl's dresser.
There is also a space family achieved by marrying a sun gotchi presented by a planet looking gotchi (in the dating show that is.) Marry that and you get a strange baby and you will get a space themed family. Or you can marry a Japanese famitama to get the space family.