When she speaks to Gumball or Anais, she refers to Darwin as "your brother." Due to Nicole's general stressful character, the fact that Darwin's outlook is to appease everyone, he is rarely the center of her wrath.
In "The Mothers," when Gumball offers to rework a sign to impress Nicole, Darwin strongly suggests just following her orders and sitting in the car, implying that he respects her parental authority.
Though Darwin is not as attached to Anais as he is to Gumball, the pair share a rather close sibling relationship.
In "The Roots," Anais tells Darwin he is her favorite.
Though the two do not seem to interact very often, Nicole sees Darwin as her own son and is rather affectionate with him, in turn he sees her as his mother.
Darwin can be somewhat clingy towards Gumball and does not like being left out most likely deriving from the fact that up until recently, Darwin has always been near Gumball and has not made many independent choices of his own.
The fact that Gumball was almost directly responsible for his evolution into his current form is likely another reason.Darwin expressed his affection for Nicole in "The Mothers" as he was determined to prove to his friends that Nicole was indeed the best mom and was very excited to tell his mom when she eventually ended up winning the competition.