Dd is just two and for the 2nd time in 2 days we've had the same issue.
Both times she has done something and I'd like her to apologise. The first time she hit her baby (12w) brother and made him cry. I said something like, 'please don't hit Ds, its not nice. He's crying now, he's sad - you need to say sorry.'
The second time I stupidly left something out and she wrecked it. No big deal - I shouldn't have left it out. I caught her doing it, told her not to and asked her to say sorry again.
Both times I asked her to say sorry she had a massive, massive melt down and was sobbing like I was physically torturing her. The first time, stupidly, it became a fight about saying sorry:
Me: say sorry dd Dd: (sobbing) no, no, no, I no sorry. <repeat>
In the end I dropped it because I was worried thr it had obviously become a battle of wills about this bloody word and I thought I probably wasn't handling this the best way anyway.
My just turned 2 year old will say sorry if told too, but it just seems to have taught her that if she says sorry straight away then it cancels out the, eg, punch she dished out to her 10 month old brother
This is why I don't force my ds to say Sorry. I say it when appropriate and sometimes he says it when it is too. Sometimes he doesn't! Because he's still learning how to talk and how to behave.
I don't want to get into a battle with him over saying a magic word. If I don't want another adult to think I'm not bothered about what he's done, I apologise and then talk to him about what has happened. It's the long run I'm concerned about.
My DS 2.4yrs is a late speaker and his vocab is still quite limited. He does however like saying "sorry", to the extent that he'll bump into us or hit us on purpose just so he can say sorry. He also says sorry to inanimate objects that he bumps into. It's quite sweet. When he is naughty we get him to sit on his own in the hallway for a minute or two. Removing toys also. He never says sorry when asked to say it but I don't think he understands yet. It will come with time. We let him know which behaviours are unacceptable. The rest will come with time - I hope!