Dear L.,
Your 3 yo is doing NOTHING out of the ordinary; she's 'testing the waters,' so DON'T PANIC!! First and foremost, don't heavily scold her in front of her friends and parents; take her aside and kneel in front of her so you are EYE LEVEL with her, and firmly and with confidence in your voice, let her know that 'SHUT UP' is UNACCEPTABLE, PERIOD. Other phrases can be used, i.e. 'Be Quiet,' etc., but YOU DO NOT APPROVE of 'SHUT UP.' Don't use a 'sweet talk' mode in your voice, but don't be a drill sargeant, either. Tell her, after you explain this to her, that she owes her friend and apology, take her by the hand, and walk her over to the friend she owes the apology to, and have her DO it. Explaining WHY she is apologizing to her friend ('I am sorry I said shut up to you') will remind her of WHY she was apologizing, and by hearing it, will let YOU know SHE understands why you are having her apologize to her friend. Then DROP it, after a hug and a 'good girl' praise from you (i.e., I am proud of you! You said you were sorry like a big girl!), and let her get on with her play. Don't bring it up again and, if it happens again, which it undoubtedly will, pull her aside, out of earshot (no need to embarass her, and you will likely embarass the child and parent who is being apologized to), go eye to eye with her, and let her know again that 'shut up' is unacceptable, and bring her over to apologize to the playmate. Your daughter sounds like a delight, but if and when she slips up, remain calm and don't allow yourself to become 'mortified.' She is a little girl, still learning, and she hasn't committed a mortal sin!! L.