Interesting topic. I'm obviously too young to know or remember cycling stories pre '90s but it seems there were a lot of such problems within a team. I exclude national teams as they most of the time in history had inside conflicts.
I know that de Vlaeminck isn't known for his good personality but his
Giro '76 display against more capable GC rider (or a better climber) de Muynck was something to forget soon. I know that de Vlaeminck somehow managed to get 4th year before while those Giros didn't shy from the mountains opposite to Moser Saronni flat Giros but refusing to let the teammates to work for technically their leader de Muynck could be crucial to them losing the Giro. Story or de Vlaeminck abandoning the same Giro by running into woods like a ekhm... street worker is hilarious.
I've heard that Phil Anderson in '80s had problems with french riders within his team which may be close to truth as in
Tour '83 he had problems with Pascal Simon. Simon did actually get the yellow and it was unknown how he would fare in the Alpes but sadly he crashed before them and later abandoned on l'Alpe d'Huez stage.
I remember in older Watts videos circa 2003 there were those two midgets having a boxing match on the middle of road propably in Giro but i sadly don't know who they were.
From other unchecked stories i've heard that in Tour '14 when Nibali was in yellow he wasn't very polite to his teammates. I doubt that this story is plausible but Nibali is a quite dodgy personality. I'm not so sure how Contador and Leipheimer were with each other in '07 and '08 as Levi was two times (Tour and Vuelta) close to beating Alberto in GC.