Ok, first off, please, please, please ignore the comments urging you to hit your child. One woman actually said "I'm surprised grandma hasn't busted her butt." Oy vey, what the heck would that teach? The only thing that would teach is that it's somehow ok for adults to hit, but not her. Seems like an incredibly confusing message to give. I'd much rather teach children that it's not ok for anybody to hit - period!
You should know that this is a very typical development for this age. I'm fortunate in that my son hasn't really been a hitter (though he has done so from time to time - and he has other things I've had to work on), but I do know that the statistics say that 50% of kids will be "hitters." Others will bite, others will push, others will be screamers (that's my son), others will pull hair, others will pinch. Even the most docile child will strike out from time to time. So, please don't be embarrassed about what is very common behavior for the age. Having said that though, I agree that it shouldn't be ignored. Things that have worked for me in the past is to redirect every single time and use the same words - i.e. "we don't hit," "hitting isn't nice," and then start another activity. If she's old enough and has words I'd have her apologize. My son has to say he's sorry when he hurts someone or takes something from them. Something else I read that's supposed to help is to ignore the hitter at the time of the offense and then make a huge deal and pay a lot of attention to the "victim." Part of the hitting is to garner attention and if she doesn't get any she may stop. There are also a # of good books out there that deal with this issue. One is called, "Hands are not for Hitting," or something like that. It talks about all the good things hands are used for and why we don't use them to hit. Finally, the other thing that has been really effective for me is to talk to my son before we go somewhere. We discuss where we're going, how much fun it will be and what behaviors are expected. I will tell him that if he does X we'll have to leave. For some small things he gets a 2 time warning and for other things (hitting for instance) he has to leave immediately. So, if we go to his gym class and he hits someone I pick him up and we go right away. I've had to do that twice and he's never done it again.
Finally, I would not ever force her to go into stranger's arms if she is uncomfortable. She may be having some stranger anxiety right now, which is very age appropriate. I don't blame her for striking out if she's scared. There's no reason she has to go into anyone else's arms and there's certainly no reason to be embarrassed by it. She likely doesn't have the communication skills just yet to tell you how she's feeling and striking out is her way of letting you know that she's not cool with something.
Hang in there, she'll be talking up a storm before you know it and it will all become so much easier.