As kids get older, naps fall to the wayside. They just don't want to sleep during the day anymore, and that's okay. It's part of them growing up. But you've noticed without the sleep, your children can get super tired, cranky, ornery or all of the above, and worse, they have no idea why or even that their personalities have changed in the slightest.
Solution:
Institute a 'quiet time' in the afternoons, where your child doesn't have to sleep, but does have to stay in her room playing quietly, reading or simply resting. After 45 minutes, if she hasn't dropped off to sleep, you can open the door and let her run around loudly once again.
Whether or not she sleeps, this time will help her calm down, center herself, and recharge for the rest of the day. If she does sleep, fantastic (so long as it's not for too long). If not, at least you've re-steered her day, so that any of the high-strung emotions she was feeling settle into a more even keel.
After this time, make sure you feed her. A snack will serve to kick-start her system back up after the afternoon siesta.