New ideas on how to discipline a toddler/child?

I have two children that are a year apart in age. I give them undivided love and affection daily but for some reason my daughter (almost 3 yrs) likes to be really mean to her brother sometimes. For a few examples, she will push him down really hard or rip out chunks of his hair. I discipline them by giving them time outs, toys taken away when they are being naughty. Do you think that she might be jealous when I spend time with the youngest or is this just part of a terrible two stage?