Mrs. Peterson was once Julian's next door neighbor and was convinced that Julian was her grandson and therefore invited him over to dinner frequently. She has also been known to purchase gifts for Julian. ("Mrs. Peterson's Dog Gets Fucked Up") Mrs. Peterson also owns a dog she has named Sparky and thinks the world of him, and entrusts him to Julian's care whenever she has to leave for an extended period of time. One day, when Mrs. Peterson thought it was Julian's birthday, she gave him Sparky to take care of while she went shopping for him under the guise of going to the hospital for outpatient surgery. Due to her fairly close relationship with Julian, she was able to note his drinking habits and his literally constant drinking of alcohol and expressed a high amount of concern for his habit, telling him "I don't like to see you drinking too much" ("Mrs. Peterson's Dog Gets Fucked Up").
Mrs. Peterson was also one of the many park residents that Ricky, during his time as the park supervisor, asked to borrow some tin foil from when he was lining Julian's trailer with it ("A Man's Gotta Eat").