Petunia is a wooden hand puppet with tan skin, short auburn hair, and black eyes with purple eyelashes. The light blue stuff on her arms resembles a spring toy. She is seen wearing blue stud earrings and a green sleeveless dress with a white collar and two red buttons in the middle.
She's a puppet given on Fritz's hand, there are several ideas what she is:
She's a split personality in Fritz's mind and the puppet is just a way to focus the personality.
It actually has a human mind inside it, but Fritz needs to move it so she can speak.
It's a substitute for his wife, who has either died or divorced him, and left him mentally shattered.
Given that Fritz has two children, Tallulah and Laszlo, the 3rd one seems more accurate, although they could be adopted. Or his wife died when they were young.
The second, while possible, is unlikely, due to Fritz generally speaking out of this corner of mouth, while he moves the puppet.
When she's goes for a drive, she usually takes the Harley, according to Grampa Bud.