This episode is a nice break from the formula of Earl helping someone on his list, that after the episode is over we will never see again. It may not have been as funny as some of the first season episodes, but was still pretty good.
When guilted into making an appearance at Dodge's Career day at school, after having ruined a previous one, the children question why Earl doesn't have visitation with his son, as Joy has always told Dodge that's who his father is. When Earl questions Joy about Dodge's father, it comes out that she's been lying about getting pregnant at a concert. Instead she says that Dodge's father is Little Chubby, but when she went to confront him, his violent personality made her think better of ever telling him.
So Earl begins an unsuccessful attempt to talk to Little Chubby, and then to get DNA to prove that he is Dodge's father. In retaliation, Little Chubby makes Earl's life misserable. Darnell eventually gets Chubby's DNA, and Earl sends it aways for evaluation.
When he confronts Joy with the results, we find out that NEITHER of her boys have the father any of the characters would have expected. The episode leaves us waiting for next season to find out who Earl Jr's father really is.