Continuity mistake: When Fred and family start their drive toward Jellyrock Park, the trailer has one window and a door on its right side (behind Wilma's side of the car), but when they reach Jellyrock that side of the trailer now has two windows and the door is gone. (00:11:50)
Revealing mistake: While Grandma Dynamite is on the roof sending smoke signals, Sonny is standing in the tree. When Sonny starts laughing we can see the bottom of his jagged clothing is now a mere straight line and his legs have vanished. (00:16:45)
Answer: The name of the pet is "Baby Puss." He has appeared in episodes, but only a very few. The first episode was probably "The X-Ray Story" from season 2.
Bishop73