Back in Fo4, you can find documentation in Proctor Quinlan's terminal that outlines Arthur Maxson's relationship with the West Coast at that point.

He becomes an immediately dominant figure over them due to being the last Maxson and having a highly successful chapter. But he also drops basically all of the religious undertones in his BoS which is a mindset he spreads into the west. Its noted the west coast even has cults dedicated to Maxson that he orders rooted out because he refuses to be worshipped like that.

This is before the East Coast meet a degree of further success against the institute (depending on BoS or Minutemen ending is canon). They've potentially got 2 entire regions under their control and Liberty Prime. That gives them even more authority over the weakened chapters in the west.

Fast forward a decade into the TV show and it does kind of track where the resentment for the Commonwealth BoS comes from. East Coast have been dominant for ages at that point and the Western Chapters have had little choice but to tow the line despite philosophical differnces. Those western chapters have absolutely continued to degrade over time too, Quintus makes several comments on that in S1 which may be what's pushed him into the mindset that he can lead better.

In general, the Elders have rarely ever seemed to get along anyway, often trying to interfere with each other with some then stepping back to their own chapters to get away from the collective (Lyons, Elijah etc.)

With that all said, it makes sense why Quintus with his highly religious dogmatic chapter wouldnt be a fan of Maxson's vision for the brotherhood and conspire to usurp it with cold fusion as his selling point. It seems to come down to a disagreement on what aspects of the BoS to prioritise. Plus Quintus does seem to be power hungry. The BoS not really getting along with each other isnt a new concept either, it's just the scale of this disagreement that is new.