I have an 8 and 6 year (girls)- I have always made them apologize to everyone they misbehaved in front of. It taught them not to do it, because they only did it a few times then learned : UH-OH, I'm going to get in trouble in front of my friends/family if I do that again. So all I can say is "Way to go" and "Keep it up". 

you did the right thing I have all my kdis say they are sorry for whatever they have done even if it wasnt done on purpose I feel if they can admit they are wrong (or when told to they can do it LOL)  they are learning to take responsibility (wow that was spelt wrong)  anyway they are learning how to act when older, after all I think most of us have know of atleast someone who doesnt take there own actions seriously and cant admit they are wrong.. and I dont want any of my kids endign up like that all becasue I let them "get away with " whatever they have done..  its works well to tel mine that the results will be much better if they say there sory then to stand there mad that they have been cought. :)  and normally I jsut do a very short time out if they have said they are sorry  and its not from what theyve done its how badly they handled the appoligy  if they do it quickly and nicely then they are told to think about what they did.. this works for my 7 and 8 year old my 4 year old has problems understand how what he does effects others still and the two year old wel lshes two LOL  its normally my fault she does something wrong eithe ri didnt watch her or defuse the situation when I coudl see it happen.... 

I make my 22-month-old apologize when she bites or hits.  She has learned to say "sorry" and "nice" (she says this while gently stroking the place she hit or bit).  I don't see anything wrong with teaching a child there are consequences to their actions.  And you're using mental consequences instead of physical ones, which will likely stay with her much longer.  You're not going to "scar" her, but you are impacting her - good for you!  As for that other mom, I wonder how bad she is scarring her own child by not following up on poor behavior.

You did not scar your child. You handle the situation well, the other mom needs some meds or something. Our job as parents is to teach children what is good and bad behavior. Also to teach a child to apologise is so important in a soceity that has become more rude and hostile each year. Job well done.

As a mother of three, I have always made my children apologize for their behavior.  If it was a disruption to everyone, I think it is important they say they are sorry to everyone there.  I think this is a really important way to teach your children that actions/behavior have consequences.  If I snap at my husband, for example, I always go and apologize once I've calmed down.  This is usually an opportunity for us to discuss whatever happened calmly.  By having your daughter apologize, you're teaching her how to respond appropriately when she misbehaves.  For anyone interested, there's an intriguing debate on discipline/spanking at www.opposingviews.com/questions/is-spanking-an-acceptable-form-of-discipline.  It's a really good debate from experts on both sides about whether to spank or not and includes suggestions for other disciplining strategies.