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I tell my children “As soon as you do ____, we can ______.” Is that bribing them?
“As soon as” should not be used as a threat. Use it to teach sequencing and let your children know where the priority lies. “Work before play. As soon as you clean your room we will leave for the park.” I would not suggest stating this in the morning as a means of manipulating a young child to clean their room at some time during the morning in order to earn the privilege of going to the park some time in the afternoon. Figure out how long cleaning the room will take, be prepared to go in and help until you are sure they can do it alone, and then decide when you want to go to the park. If cleaning will take 30 minutes, then 45 minutes before you want to leave tell them, “As soon as you’re done cleaning your room we will leave for the park!” and get them excited. If it’s helpful, set a timer so they know how long they have.

As for leaving places – I decide what I will accept, what is reasonable and what I will do. Then I teach them those expectations, and am willing to leave when they aren’t able to meet them. It’s not punishment, it’s to keep me from being overwhelmed. It’s to keep their behavior acceptable and keep them successful. It actually prevents punishments if I’m willing to leave rather than try and force them to do what I need.
It’s important to make your expectations clear, and if they don’t live up to them, you leave. Honestly, I’ve only had to do this a handful of times, but doing it is what makes it clear that your words have meaning. During the rough times, I started taking a double stroller with us. I could carry one child and put two others into the stroller if I had to. Even though I rarely had to do this, I felt more on top of things with that option, if it came down to it.
Also, there are two things we worked on that made these incidents rarely occur. One is the idea that, “Leaving successfully is part of coming next time.” I explained that it’s not worth taking three children out someplace if I have to fight with someone to leave. Especially with the things we did on a regular basis, I would remind them that leaving well today was required for us to come next time, and if they made it not worth the effort to me, we’d stop going. The other thing was practicing what I expected for leaving. When we’d go over rules before we went in somewhere – always including, “Listen to Mommy’s words,” as the most important rule – I added, “And when it’s time to leave, I expect you to say, ‘Yes, Momma,’ in a pleasant voice and come without fighting me.” We’d practice the dialogue a few times, and it only took a few times with a reminder. Now, even if I forget to review this in advance, I can say, “Oh, how do we leave?” and they stop and say, “Okay, Momma!”