Thanks to everyone for the suggestions. This is helpful.
I'm reluctant to go into the specifics, because: 1) its complicated; we've had over a year's worth of wrangling, on many different issues. and 2) I might share this thread with other members of my group, as a helpful resource; so I want to be careful to not hurt anyone's feelings, or to paint things in a one-sided light. I admit that it takes two to tango -- I have regularly fallen into a wrangling dynamic, and I feel demoralized about it.
But to whittle it down a bit: it's not player-vs-player conflict, and it's not about outside politics; it's entirely between me and the other co-DM; we take turns DMing and playing different adventures. (Our D&D club has five members, including myself.) Our arguing has mostly been about rules; and especially about:
1) playing straight RAW vs. bringing in houserules and tweaks (e.g. revised Shield Master feat)
2) low-magic vs. high-magic (magic-item rich)
3) in a group with two co-DMs, using a shared ruleset, who is the authority?
Now, we have had a good deal of fun over the past year, but these sore spots (about different values, different understandings, and different needs/wants) have built up, and I sometimes don't look forward to playing anymore. We're taking a week off, to help soothe frayed ends.
Last week we argued about numerous topics, for a long time. This time it happened after the game.
A few days later, two players (my fellow arguer, along with another player, who was trapped there listening to us argue, waiting for a ride home) both voiced an idea of adopting 'table rules' about arguing. Basically an Argument Protocol: a protocol for stopping arguments. And that sounds like a good idea -- a positive stride forward.
So I'm doing 'due diligence'. What would such a protocol entail? (The idea about 1 minute time-limit sounds like a good start.) I've gotten a helpful spectrum of advice from ENWorld fellows before.