Hello B.,
My son just finished with this stage. Yes, it does go away if dealt with in an appropriate manner. She probably is around lots of kids during work hours where she learned this behavior. It is very important to use the words "gentle" with young children. I had to catch my son's hands as he tried to hit and remind him too many times that "I love you and I do not hit you so please do not hit me". Maybe explaining love to her will help. You would be surprised at how much a 2 year old understands if it is constantly reiforced. Make sure that you let her know that you love her and do not hit her so please do not hit me. It helps to also tell children that it hurts you when she hits.(they understand ouchy or booboo) Follow it up with I do not hurt you so please do not hurt me. Sometimes I even over- exaggerated when he hit me to let him know that it hurt.
As for timeout, it is not a place where they can have the limelight. Just like the bedtime ritual constantly putting the child back 5 times. I think it is appropriate to use the child's age as a timeframe for timeouts. My son knew that after 2 minutes he was finished but it was the longest 2 minutes of his life.
Parenthood is awesome isn't it? I never knew I had this much learning to do...But it's fun! May you conquer this battle and onward to the next. Good luck, B.. M.