I've never really got this one down. family background is extremely fractured and really rather unpleasant. When I get angry, really angry as opposed to cross, I have trouble dealing with it. Either I crumble and then get the shakes and red mist later; or I say exactly what I am thinking at that point which tends to really mess things up. Unforutnately then I assume the other person will never want to speak to me again (old conditioning) which means it's hard to talk it out.
On the occasions where I do keep calm and reasonable, sometimes it works and sometimes it doesnt. Its taken me all these years to realise that actually, quite often it's the other person as much as (or more than) me. Their problem more than mine. Not always ofc, but its not automatically my fault as I used to assume.
Recently I've had to go NC with a family member due to some extreme, and according to my husband completely unwarrented, nastiness on her side (I think she's taking something out on me that has nothing to do with me, at least that's the only explanation I can come up with else I'm at a loss). Even though I can tell myself it's her problem, not mine, the near-hate in these communications has shaken me badly and 5 months after cutting contact it still haunts me. Angry, puzzled, hurt. Still don't know how to handle the strength of the emotions and get it out of my head.
So I'm sorry, but I hope you can find more of an answer than I can. Maybe it will help to know that some of us flounder completely! :) But I hope you can find a more constructive and helpful way.
Someone wise once said to me that anger gives us the strength to take action over something that needs to be put right. Wise words.