How can I teach my toddler the meaning of the word "no"?

[Cindie]

My 15 month old has always been very agressive towards other children. I now have a two week old and I'm having a terrible time getting her to listen to the word "no". I know she gets what's right and wrong by the way she goes directly to doing what's bad when she wants attention. Distracting her is out of the question because she just goes right back to doing it and when I have to feed the newborn I don't have the hands to stop her. I tried making her look directly at me and saying it sternly, she thinks its funny. I've tried a time out chair, but even when I keep her there crying for 5 min she goes right back to doing these bad things....ex; grabbing baby, banging toys on the tv screen, climbing on the coffee table. I even tried slapping her hand, which I was going to avoid doing, and even though I know it hurt, she still went back for more! I feel like I have an impossible child! I know these things are done to get attention, but they need to stop! My husbands in iraq so its just me doing the dicipline. Shouldn't children at this age understand the meaning of "no" by now? Does anyone have any tricks they used to get their child to behave at this age?