Conflict on the playground

I thought my biggest worry with Elizabeth, for the moment, was going to be teaching her not to hit, pinch, and pull hair. She does all three of these - a lot. She actually came home from school on Thursday  this week with a nasty bruise from a bite - her teacher obviously didn't tell me who did it, but did let me know that Elizabeth had been pulling hair and pinching faces all day, so it may have been provoked. So I thought we just needed to teach her to stop hurting her friends (and us) and that would be that. If only ...

Today, while Elizabeth was playing on the playground equipment at Central Market, I discovered a new problem. A little 2-year-old girl took a liking to Elizabeth and followed her around trying to hug her and pet her arm and play with her hair. All perfectly innocent, except that Elizabeth doesn't like being touched (or talked to, really) by strangers, of any age. She'll say hi from the safety of my arms (if she's approached carefully and without too much fanfare), but otherwise she usually just stares people down who want to talk to her or touch her. 

That's what she did today. This girl kept following her, and Elizabeth kept edging away until, not wanting to look like a jerk of a mom since the other girl's mom was right there, I said, "Elizabeth can you give her a hug?" She very nicely complied, then tried to get back to playing - but the other little girl wouldn't leave her alone. Finally, when the other girl tried to play with her hair, Elizabeth had enough and slapped her in the arm. I had to say "no, we don't hit," and apologize to the other mom, but really, I was cheering that Elizabeth had stood up for herself and knocked the other girl away. 

So here's the worry. I don't want to raise Elizabeth to be anti-social, anti-touch - but at the same time, I want to teach her about personal space and respecting her own and others' boundaries - which is obviously hard when parents encourage their kids to keep chasing mine down for that hug. So what's the solution? How do you raise a toddler with limited reasoning ability to be able to reject interaction with others when they want, without just being rude?