S.G.
A lot of kids go through this as a way of communication. When my granddaughter was going through this stage she got a time out at home or at my house for it also, but what seemed to make the biggest difference was I would hold her hands gently and tell her "Grandma doesn't like to be hit, she would much rather have hugs and kisses" I repeated this anytime she would hit and she would always give me hugs and kisses. I remember one time in Walmart when I was pushing her in my cart and I had to say this, she would pull me down to her every 2 minutes or so giving me lots of hugs and kisses. I think one time her mom spanked her when she hit her and she looked at me like "are you going to let her do that?" I said "your daddy would probably got a spanking too if he hit me" She accepted that and I don't think she hit after that. I would never suggest spanking because I believe that should be a last resort disipline, but try the "I don't like to be hit, I would rather have hugs and kisses".