[rsync]

"We like to say that people (especially children) shouldn't be punished; they should only be rewarded."

I think neither is correct. I think this is a tactical decision that needs to be made in the moment based on time and energy.

Which is to say, it is neither correct nor incorrect to slowly, agonizingly, peel off a band-aid. This can be a successful strategy. Sometimes, however, you just need to rip it off and get on with your life ...

(three kids)

[tremendulo]

Yes. I don't think one can escape from the fact that punishment and reward go hand-in-hand. By the contrast principle, absence of reward is logically equivalent to punishment. Even without explicit rewards and punishments, children will pick up their parents' emotions. And if there are no emotions to pick up, the child will choose another parent figure. Because children want to grow.