Should I make my child apologize?

Performance. A child who is told to say sorry learns the sound that ends the trouble, which is a genuinely useful thing to learn and has nothing to do with repair.

Janet Lansbury puts the mechanism plainly in Helping Our Children Say "I'm Sorry": when someone feels attacked, judged, or under demand, it gets "really, really hard… to get to that place where I can genuinely feel regret." Children are no different. The prompt lands at the precise moment a child is most defended, and being defended is the state least compatible with the feeling you were hoping to produce.

They will, from watching you. Of the three routes by which families transmit emotional skill in Amanda Sheffield Morris and colleagues' 2007 review, the deliberate teaching route is the smallest. The one that does the most work is the one nobody is running on purpose: a child copies the method they see used, and no instruction is required for it to land.

Lansbury's version of the same point is that a child watching a parent apologize out of real regret will overrule anything that parent tells them to say. So apologize to your child when you get something wrong, out loud, unprompted, including for the small things. How to give a real apology is the shape of the thing you're modeling. Well, what do you say? isn't teaching. It's a cue for a sound.

Then you apologize. Out loud, to them, in your own voice: I'm sorry that happened. That must have hurt. The waiting child gets the repair they're owed, the other adult sees the situation taken seriously, and your own child watches the whole thing from two feet away, which is where the learning was going to come from regardless.

What you're skipping is the standoff where four adults wait for a small child to produce a word under pressure. Nobody in that scene is learning about repair. They're learning about the standoff.