This!
While the dynamic you described differs in a lot of ways from the dynamic I've found with my partner, banishing this kind of behavior from our relationship early on was an absolute game changer.
When we're upset, we ask three things.
1. Does it need to be said?
2. Does it need to be said by me?
3. Does it need to be said right now?
If it gets three yesses, we discuss it dispassionately. Because we are partners, not competitors.