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should you even avoid telling them to go away or go in the other room, if for no other reason to allow YOU to calm down?

No. In fact, I think that putting some time and distance between yourself and your child until everyone's cooled down is the smartest thing you can do.

I often find myself ready to pronounce a really stupid disciplinary action that I would regret later on (like taking away privileges for much longer than I should) when I'm angry. If we all get some time to cool down before it comes to discussing disciplinary consequences, sometimes we can solve the problem without any disciplinary action at all, simply by talking about what happened, and why. I feel much better with such a resolution (unfortunately it's not always achievable).

So when my kids fight among each other, or there's a conflict with me that angers me, I've started separating the kids/us. The easiest way is sending them to their respective rooms for a while, where they have something to do, but I don't really care where I send them, as long as they're separated from the source of the conflict. When it's nice outside, I often send them to play outside for a while.

I don't view this as a punishment, even if my kids might disagree or say it's unfair.

As far as it being unfair: I guess I could just as well remove myself and let the child remain where it is, but usually what the child is doing can be done somewhere else, while what I'm doing requires my presence (e.g. playing with a toy vs cleaning up the kitchen), so it's the child that has to move.

Here's a bit of honesty, though: I'm having trouble with the idea of removing myself from conflict on principle (as opposed to now and then, when I'm so angry that if I don't leave immediately, violence might follow). Our home is not a tyranny, but it's also not a democracy; and while it might be fair to say that getting angry at my child is my problem, not the child's, and therefore I should remove myself instead of the child, I have a diffuse feeling that doing that would be a bad idea, especially if the child behaves in a clearly unacceptable way. I guess there are too many specifics to explain exactly why I have that feeling, but most of it is connected to being able to wield authority and enforce rules.