19 month old DD aggressive with other kids - please help!

[catanddog]

I have a DS 4.10 and a 19 month old DD. DD is a bright and cheerful little soul at home, who knows her mind but is lovely to have around. Her and her brother play brilliantly together and there's virtually no arguments over toy sharing etc, and certainly no fighting. She has lots and lots of words and understands pretty much everything we say to her.
However around other kids (normally her age/size) both at home and out and about she is a complete nightmare. She can't share anything, and runs around screaming "mine mine mine" if another child has a toy she wants, this would be ok but she will lash out at random kids (completely unprovoked attacks) coming up behind them and hitting them, or just grabbing them by the hair and pulling them across the room or to the ground, lots of shoving of other kids etc etc.... I know she's still very young, but it's getting to the point that I'm reticent to take her to playgroups etc as I just can't face what she'll do next. At home we introduced the naughty step a month ago, which seems to be exclusively used for hitting incidents, or just coming down to her level and telling her a firm "no" and "to play gently/nicely" and I always ask her apologies to her poor victims which she does, and then within 2 minutes she'll be at it again. I've tried ignoring it, and praising her when she plays nicely, but still nothing.
No idea where she's picked this behaviour up from, we are not smackers at home and my DS is a normal active kid but not aggressive at all.

Help me please!!

Can you hover over her at groups, to the exclusion of even chatting? I know it sucks, but those groups are your best opportunities to teach her to share & tolerate. I think she's too young for N-Step or "punishment". When she goes to be aggressive you prevent it or give the disputed item to the innocent party. If she has 2+ items let her choose which one to share, that kind of thing.

I want to keep taking her to these things, and I watch her like a hawk and step in at the first sign of any aggression, but it's just becoming a nightmare as it's so stressful and I dread even taking her to childrens' parties or anything of that nature. I feel the N-step for the minute I have to keep going with as it just gets out of control if not. We had some friends over yesterday with their 2 of a similar age as both of ours, and she must have actually hit/shoved their 2.2 DS about 30 times, let alone the "attempted" attacks that we interceded - it just is so embarrassing.

yeah, I know, btdt. :(