at each other's throats

be at each other's throats (over sth) (in angry disagreement; arguing or fighting) — враждовать, находиться в состоянии (непримиримой) вражды; (постоянно) ссориться, конфликтовать

Example 1: The neighbors are at each other's throats over who should repair the fence.(Cambridge Dictionary of American Idioms)

Example 2: Still, my mother and I fought a lot when I was a teenager. When you're a teenager, you think you know better, and in my early teens, I resented her at times. We were just a normal family: Mother and daughter at each other's throats! (Cosmopolitan)

Example 3: It was a very dramatic trial, with the prosecutor and the defense attorney constantly at each other's throats. (answers.com)

see also

at loggerheads
[at daggers drawn]
at odds/at war
on bad terms

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This idiom, with its vivid image of two persons trying to strangle each other, is often applied to less physical forms of disagreement.