My friend had this problem with one of her kids and she asked me what to do about it, as she had tried everything. I don't suggest hitting (that just teaches them how to hit too. They model our behavior, as you've found out.)
Anyway, my friend did what I suggested (because I did this years earlier and it worked for a kid that I was a nanny to at the suggestion of the mother) and it worked for my friend too. I would use apple cider vinegar. Yes, very nasty for kids. All you do is stick your clean finger in the bottle and get it wet and wipe it on the tongue of the child. That child does not get anything to drink for about 5 minutes. It should work well. When I did this (at the request of the mother) it was with a spitter and he stopped after the 2nd time. With my friend, her child didn't bite another child until about 2 weeks later and she did the vinegar a second time and her daughter stopped...never to do that again.
I know this may sound weird or even harsh, but ACV is good for you, but quite nasty. lol I've never done this with any of my children, as I've never had this problem, but if I had ever had that problem, I would use this method.
Good Luck!
40yo Mother of 4