[Inziladun]

Well, the "histories" given in the Appendices of Arnor and Gondor were supposedly obtained by the hobbit authors, and I would suspect that at the time of the War of the Ring much more was generally known about the history of Gondor than of Arnor. That's borne out, I think, by the fact that the Heirs of Elendil existed for so long unnoticed by most. Probably in the archives of Minas Tirith there were more details of the disunion of Arnor, and maybe at Fornost or Annúminas, but who had searched them?
Oh, Gandalf, Elrond, and likely Aragorn knew some more information about the matter, but it just doesn't appear to have been a major concern of the hobbits to go into detail about it.

As for why the sons of Eärendur began fighting, maybe it began out of a petty dispute about the way the kingdom was being run, and was escalated by personal grudges and jealousies. That's pretty general, I know, but RL kingdoms have been known to fall from such small beginnings.