Lets ignore all mussar and the horrible things Chazzal say about anger. Let us also ignore that humility is one of the seven qualities a judge needs. And we will also ignore the chillul Hashem that can come out from a judge behaving like a child.
Instead I will quote the one source I think may shed some light on this, but keep in mind your situation is not explicitly mentioned.
The Shulchan Aruch in Choshen Mishpat siman 7 siff 8 writes 'Two talmidei chachamim that hate each other are not allowed to sit on a court case together. Due to the animosity between them, each one will put his mind to undo the others words.'
This is not a psul in the judgement bidieved, but the language used lichatchila is a strong one of psul.
The important thing to remember is that in laws such as this, the qualification for hate is to have not spoken to each other in three days, out of this animosity.
The Aruch Hashulchan in siff 17 adds 'and the outcome of the ruling will not be true. Also do not appoint two people who's personalities are different in their nature and dealings (seffer hachinuch).
The common theme is that what we've got here is a failure to communicate, which translates as a psul, lichatchila at least, for judges who need to be able to communicate with one another and the litigants. An angry, argumentative person disrupts the system of justice from being carried out to its truthfulness. Especially if his outbursts cause the other judges and or the litigants from speaking their mind.
Disclaimer: I'm not certain the psul mentioned applies to ZaBL'A and a case of pshara krova l'din. But the idea as least seems to hold up.