I'm with madb

If DD (more than DS as he does understand) hurts someone, or even the dog, I show sympathy and apologise myself. She kind of looks on and then realises what I'm doing on her own, without being made to apologise. She then offers her own apology and shows a bit of remorse for doing what she did.

DS thinks the world revolves around him, which is really frustrating, but he only really apologises when he can see if something is really serious.