As an elementary school teacher, I can say you should focus on the positive. Point out all of the *right* things that they are doing and tell them, "Olivia, I really like the way you did that." Or, "I'm so proud of how you put away your toy after you were finished. That's awesome!" When they start whining, tell them that you want them to speak in their "big girl" voices. Then praise them for using big girl voices (especially if you didn't have to tell them to at a time when they normally would have whined). The first few days you do it, think of yourself as a cheerleader for the day. Pretty soon, it'll be natural!
Some type of reward chart will really get the kids excited about all of this positive behavior (whining is negative behavior). Watch a SuperNanny show to get ideas - or Nanny 911. They do a great job of using reward charts. Every time you think they did a wonderful job doing something, say, "I'm so proud of you! You've just earned a star (or whatever) for doing that."
Introduce the reward chart during a calm time of the day. Tell them the very simple rules of the house, like (1) Use big girl voices (no whining), (2) Use loving hands (no hitting), (3) Listen to Mommy, etc..... whatever you think they need. But, keep the rules simple and short. 3 to 5 rules should be enough.