Planet of the Moms is a planet Timmy wished up in Invasion of the Dads. At the end of the episode, all the dads started crying because Timmy's mom left. Timmy wished this planet up to make them happy as well as prevent them from trying to take his mom away again.
Similar to the Planet of the Dads, it is inhabited by several clones of the parent the planet is named after; in this case, Mrs. Turner.
After Timmy rescued his mom from the Dad clones, they began to greatly miss Mrs. Turner, so Timmy wishes up the Planet of the Moms to keep them happy and prevent them from kidnapping his mom again. Later the moms invade Earth to steal Dimmsdale's kittens, but were foiled by Mr. Turner and his monkey wrench and forced to leave.
The planets of the Dads and the Moms
The dad clones celebrate as the planet of the moms got wished up.