Make rules clear up front...and punishments, too
Telling your babysitter what is, and isn't, permitted can go a long way toward making the night better for all -- as can letting your kids know she's the one in charge. Announce bedtimes in front of everybody to cut fibbing off at the pass. Also, be sure the sitter knows what types of punishments you practice: time-outs? Loss of TV? Be specific about what you want her to do if your kids aren't angels. Slacking on the rules when she comes actually makes her job harder.
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No money, no problems
Rule #5: We don't argue about money
Goal: Short-circuit begging and pleading for stuff
This rule has to be enforced consistently to work, but the basic deal is that you can tell your child yes or no on any requested purchase, but you don't discuss it. If your child protests, simply repeat, calmly, like a mantra, that you won't argue about money. The key to success is that you have to have the courage of your convictions and not argue. Thus the calm repetition.
It cuts both ways, though: When your kids want to spend their "own" money, point out potential mistakes and give advice on the purchase if you'd like, but at the end of the day, don't overrule them unless it's a matter of health or safety. After all, you don't argue about money. They may make some bad choices, but they'll learn. And you'll all enjoy shopping together a lot more.
Why it works: It shifts the focus from the whined-for treat to financial policy. You're almost changing the topic on them, no longer debating why they should or shouldn't have gum or some plastic plaything and, instead, invoking a reasonable-sounding family value.
Rule #6: I can't understand you when you speak like that
Goal: Stopping whining, screaming, general rudeness
This one requires almost religious consistency of application to work effectively. But, essentially, you simply proclaim incomprehension when your child orders (rather than asks) you to do something, whines, or otherwise speaks to you in a way you don't like. Whispering this helps; it takes the whole thing down a notch on the carrying-on scale. This is a de-escalation tool, so calmly repeat the rule a few times and don't get lured into raising your voice. A child who's whining or being rude is clearly seeking attention and drama, so use this as a way to provide neither.
Why it works: It empowers your child by suggesting he has something valuable to say (if he says it nicely) and allows you to completely invalidate (i.e., ignore) the rude presentation.
Rule #7: There's no such thing as boredom
Goal: Prevent your child from saying "I'm bored"; teach her to entertain herself
A friend of mine says this is one of the few things he got right with his kids. The first time his older daughter claimed she was bored he simply denied that the thing existed. Now he sometimes adds: "There's no such thing as boredom, only failure of the imagination" or "...only mental laziness." Surprisingly he's never gotten the "There is too boredom!" argument, only an exasperated "Da-ad." Regardless of the phrasing, the result is the same: The burden of amusement lands directly on your child, which is precisely where you want it.
Why it works: By the time your kids have figured out the puzzle of how something that exists can also not exist, they won't be bored. Also, it changes the terms of debate, from a challenge for you (list all my toys, then cave in and let me watch TV) to one for them. Besides -- if your child learns how to entertain herself, there truly is no such thing as boredom. And that's a gift that will last all her life.