Usage patterns
〈人〉と〈人〉が不仲だX and Y are on bad terms
Those two have been on bad terms for a long time.
〈人〉と不仲になるto become estranged from someone
I became estranged from my older brother over a trivial matter.
〈人〉の不仲the strained relationship between two people
The discord between the parents can sometimes affect the children.