No. Dale never becomes aware that his wife is cheating.
When Dale realizes that he did not have séx with Nancy anywhere near the time Joseph was conceived, he becomes convinced that a space alien is his son's real father.
At Episode 4.21: Nancy Boys, Nancy sleeps with Dale again after Hank takes them on a double date with him and Peggy. While Nancy and Dale sleep in each other's arms, John sneaks into Nancy's bedroom--and is shocked to find Dale there. Dale, thinking John's a burglar, hits him with a lamp and knocks him out.
The next day, Dale goes to apologize and offers to help John fight the government over illegally seized Indian land.
Everyone knows about Nancy cheating on Dale but they just kept it to themselves and didn't tell Dale.
In the 38th Episode: Peggy's Headache, Peggy finds out that Dale‘s wife Nancy is having an affair with John Redcorn. She was so horrified that she decided to tell Dale about it.
However, when she saw how truly loving Dale is to his son and realized how exposing the truth will shatter the family. Peggy has a change of heart, and decided the matter is best left unsaid.
Learn more about the Hills and the rest of the Arlen, Texas folk by checking these 15 Texas-sized facts shared by Mentalfloss.com.