Or it might turn them into diplomats. I sometimes apologise just to keep the peace. It's not a terrible tactic. Also, sometimes things are misunderstood, or things get a bit tetchy, when it wasn't intended, and maybe an apology can just be a recognition of a misunderstanding. For example, I'm sorry you misunderstood me (even though I was right) - this still reflects a certain sadness that the exchange became aggravated.
I don't know. I can understand your annoyance, but sometimes, it's not too bad to be diplomatic. Will it help restore relationships so it's easier for the kids going forward? It might.
But then again, there might be times when it's right to stand your position and not budge - and that's a judgement call on your part - and the children's part. I hope you all feel, however you respond, it was the right thing to do after it's all blown over.