Durwood Cuyler is a member of the Cuyler family and most likely the brother of Early and Lil as Rusty called him uncle though this may because country people sometimes refer to male relatives as Uncle. He is shown to be more intelligent than his family as he got his GED and left Dugal County and later got married to a woman named Fiona and had two children named Parker and Posey. Similar to Dr. Bug he is being ashamed of his Cuyler heritage as he wears clothing and puts on facial makeup to appear more human like to hide his green (greener than his family) skin. However, deep down he shows some similarities to his family as he is unemployed and requires a welfare check for his family to get by and calls it "Greeny leafy spending money". He also shows a dislike for his wife's father who threatens to hunt him sometimes in a joking manner or in a serious one.
Durwood may be a closet homosexual as he went to an all male strip club. However, he had women porn sites on his laptop so he may at least be bisexual. In addition, he came home taking off his "make up" and clothes apparently wanting a romantic moment with Fiona. He was shown hurt and upset when he discovered Rusty and Fiona having sex; repeatedly calling her "whore". So he is possibly a closeted bisexual.