First, help your older child learn to watch what he says around his little sister. Explain how she wants to be just like him and therefore imitates him, which is why it's important for him to show his sister acceptable ways to communicate. Then sit down with your children and develop some "family rules" about words. Let them know they can get angry or frustrated, but that it's not okay to use hurtful, inappropriate, or rude words, and brainstorm with them words they can use instead to express themselves.
But if, despite all your good efforts, your child continues to call her cousin a butthead or tells people to shut up, try to respond matter-of-factly. Children crave our attention -- be it negative or positive, and a big reaction makes them think, This worked great. I'll have to try it again! So the less emotional you are, the less rewarding it is for your kids to use that word again. In a serious, calm voice, tell your daughter, "It's not okay to call people names. It hurts your cousin's feelings."
Then help her express herself in more acceptable ways. For example, you can say, "I know you're angry with Emma for taking your doll. Let's ask her to return it." Remember that toddlers are still learning about impulse control, so slipups are expected. But with a calm and consistent response from you, your kids will eventually choose the more appropriate words.
Originally published in American Baby magazine, September 2004.