A general term that might apply to this specific situation is infighting.

From Merriam-Webster:

Main Entry: in·fight·ing
Pronunciation: 'in-"fI-ti[ng]
Function: noun
1 : fighting or boxing at close quarters
2 : rough-and-tumble fighting
3 : prolonged and often bitter dissension or rivalry among members of a group or organization <bureaucratic infighting>