You apologize right now. I don't care if you don't mean it. You apologize.
Think about this.
What are we really saying to a child when we say that we don't care if they mean what they say? There is only one thing we are teaching children to do by saying this. And that is to lie.
Isn't that the definition of saying something and not meaning it?
Simply ordering children to apologize for something is not very effective at all. The best way to teach children how to apologize is to model it. Find reasons to routinely apologize to children in a meaningful way. As a father, I apologize to my daughter as often as I can. As a teacher, I apologize to my students too, and I have found modelling to yeild successful results from both my daughter and my students.