The phrase "as a quarrel between" is correct and usable in written English.
It can be used to describe a conflict or disagreement involving two or more parties.
Example: "The discussion escalated quickly, evolving as a quarrel between the two factions within the organization."
Alternatives: "as a dispute between" or "as a conflict between".
In framing the debate as a quarrel between an aspiring Kennedy-like politician and his radical activist girlfriend in the 1970's (and taking her side more than his), the movie makes an honorable attempt to enshrine the impassioned idealism of an era that has faded into "Forrest Gump" nostalgia.
Bell presents Cantor's relationship with his father as Oedipal, Cantor's differences with Kronecker as a quarrel between two Jews, and Cantor's madness as Romantic despair over his failure to win acceptance for his mathematics, and fills the picture with stereotypes.
Rome spent the 280s bc putting down unrest in northern Italy, but its attention was soon directed to the far south as well by a quarrel between the Greek city of Thurii and a Samnite tribe.
Although Orderic Vitalis describes it as starting with a quarrel between Robert and his two younger brothers, William and Henry, including a story that the quarrel was started when William and Henry threw water at Robert, it is much more likely that Robert was feeling powerless.
He acts as go-between in a quarrel between Mr. & Mrs. Bassillero.
Well, some examples, later on in history there's a quarrel between Athens and Megara as to who controls the island of Salamis.
As this played out this afternoon, so did a quarrel between two friends on the network.
He avoided committing himself in a quarrel between his cousins, the Holy Roman emperor Rudolf II and his brother Matthias, who eventually succeeded Rudolf as emperor.
The precipitating cause was a quarrel between Locris, abetted by Boeotia, and Phocis.
The riots flared following a quarrel between Christians and Muslims after Muslim prayers last Friday.
