Speaking of apologies, have you noticed that when kids say sorry, they think it's enough & then act like you're the bad person for still enforcing the consequence?
"but I said sorry "
Yes, I accept your apology, but when you chose your behavior, you chose the consequence too.

And sometimes we can feel like their apology is really touching & genuine so we don't follow through on the consequence. That's a big mistake if you're trying to reduce future likelihood of occurrence of the target behavior.

So here's the science I teach parents. Treat apologizing as a separate behavior, let's say taking responsibility, which you'd like to see more of. Reinforce that. "I see you're owning up to your mistakes more these days, good job".
Then still follow through with the consequence.

Eg: toddler flings iPad, you tell them that when they choose to fling it, they're choosing to lose access to it. They fling it, you put it on the shelf. The cry & say sorry. Giving it back in response to sorry is teaching them that sorry is all they need. Flinging will continue.

Following through looks like accepting the apology, letting them know you understand they were frustrated or whatever else. But iPad is gone, cos when they chose to fling, they also chose to lose access. They chose the consequence & you're going to respect their choice.

You can then give it back later or they can earn it back, but they don't get it as a response to sorry. Or as a response to a tantrum. Once you can get your child to understand early that it's their choice that determines the consequence, you'll reduce all of y'alls stress levels

If it's an older kid, same principle.
I let you drive my car, you must be back home by 9. If you choose to come back after 9, you're choosing to lose access to it for the next month. They come back at 9:15 there's no fight. Welcome back my love . I have to respect your choice

"but I'm sorry I came late"
Yeah, I know you're sorry & I accept your apology. However, I have to honor your choice. Because I love you. Let's hope when you regain access next month, your choices reflect your desire to have continued access. No yelling. We're in upstairs brain.

If your child is acting like they don't get it & they're mad that you're not accepting sorry. Maybe they're a visual learner. Get an egg, drop it & start saying how sorry you are to the egg. Ask them if sorry can unbreak the egg or erase the consequence.
Sorry is not a magic fix.

Remorse is great & we want to teach kids to take responsibility for their mistakes & find ways to make it better. So when they say sorry we ask them what they're really sorry for. Mistakes are how we learn & they'll make many. But we can't let them use sorry to avoid consequences

Changed behavior is THE apology. Not all this "shebi I've begged you nau why are you still vexing, is that why you're overreacting" that we adults have come to accept as normal behavior. If your not course correcting, feel free to keep your sorry in your pocket.

Somebody said what of babies. Same principle. Baby bites you while suckling, you say a stern no, put your breast back inside your bra & count to 10 or 20 whatever is age appropriate. Reintroduce it with a stern "no biting". A baby old enough to bite can make the connection.

If it doesn't work at first, gradually increase the time + remove immediately. You need the child to get that denied access is the consequence that immediately follows the inappropriate behavior. It's negative punishment & it's extra effective cos it teaches replacement behavior.

It's a science, guys. I have a degree in Behavioral Science, I spent years learning this stuff & I love to share. My specialty is simplifying the complex science, so you can apply it to your everyday life. You can find some free resources on my website http://www.behaviorcoachg.com