On page 498 of his Anchor Bible commentary on II Maccabees, Jonathan Goldstein speculates that the break between Onias IV and the Hasmoneans occurred after their battle with Nicanor.
When Alcimus was installed as high priest, the Oniads and the Hasmoneans found common ground, for they did not want Alcimus to be high priest. The Oniads believed that they should have that position, which they had for some time. But after Nicanor was defeated and the Hasmoneans gained control, the Hasmoneans did not appoint Oniads to the high priesthood. Rather, they established a Hasmonean high priestly line. At that point, according to Goldstein, there was a break between the Oniads and the Hasmoneans, and Onias IV went to Egypt and established another sanctuary.
The question of who should be high priest permeates various histories of the time of the Maccabees. I Maccabees is considered to be Hasmonean propaganda. Josephus was a Hasmonean, and so his depiction of the Oniads is not all that positive. II Maccabees, according to Goldstein, contains a memoir of Onias IV. Goldstein argues that II Maccabees is favorable in its portrayal of Judas Maccabeus, but it is not pro-Hasmonean by any means. I wonder why. Was Jason the Cyrene, the one who wrote much of II Maccabees, pro-Oniad? I could not find much scholarly speculation about who Jason the Cyrene actually was, let alone what his political leanings might be.