curious kind of discipline you have in mind.

Time-honored punishment: revoke various privileges for periods of time until they get it.

In this case, seems pretty topical to just take the phone away entirely for a few days.

When kids break the rules about screen time, there are consequences.

Not Dad fiddling with the settings, but instead Dad teaching a lesson about respecting the rules, and doing what you said you would do (children agree to obey the time limits in order to have access to the device).

How Dad should teach the lesson varies by family and by child.

Is it okay if Mom teaches the lessons about respecting the rules?

It's okay, she's just less effective.