Best Answer - Chosen by the Asker
"After the quarrel, they went to their (respective) rooms."
Although the verb "go" (past tense, "went") is very simple and plain, I think it's the best verb to use, and the one that most native speakers would use.
In the Phrase and Sentence Dictionary of Spoken Russian (Dover Publications), the following example is given: Вы опоздали, все уже разошлись. - You're late; everybody's gone already.
The Oxford Russian Dictionary gives this example: Мы разошлись по своим комнатам. - We went off to our respective rooms.
The word "respective" is optional, but if used, emphasizes that each person went to his or her own room.
The word "off" is also optional.
