Peter asks: How do you handle fighting siblings?

It turns out that the kids have entered the "That's mine!" "Don't touch that!" "Give it back to me!" "Stop it!" "Leave it alone!" stage. (For some reason I assumed this yell/cry phase would start later than four and two, but I was wrong.) Not only are they verbally fighting over random toys, treats and pretty much anything else that one has and the other doesn't, but they're also physically fighting — pushing, shoving, smacking, pulling hair, biting, etc. Siblings obviously fight and hurt each other — we get that. But we seem to disagree on how to stop it.

Peyton is generally the one who starts whatever the fight is about (because she wants whatever her big sister has), and she's the one who almost always throws the first punch. I'll be honest — I've told Addy to smack Peyton back when Peyps hits her. I figure Peyton will get a taste of her own medicine, and she'll quit bullying Addy, who generally just takes it, cries, yells for one of us, then accepts Peyton's apology and hugs and kisses her when we force her little sister to say sorry.

Lisa doesn't agree with my methods. She knows that I don't condone fighting; I just don't want Addy to be a punching bag. However, she worries that if a kid smacks Addy at school, she'll end up smacking back instead of telling a teacher. (We clearly don't want that happening.)

That leads me to this question: How do you deal with siblings (Addy and Peyton's ages) who fight?