Right around 3 our DD8 was quite the little negotiator, but what was surprising was how constructively she did so at times. We were always really good at explaining why she couldn't do certain things, and sometimes she'd propose an alternative solution that met our requirements and got her what we wanted, and it was like, "Wow. What a great solution. Why didn't we think of that?"

By that time, DW and I had laid a lot of groundwork that paid off... DD already felt empowered to make certain decisions on her own (what to wear, what to eat, activities, etc.), and DW and I had endlessly coordinated our responses on everything, so consistency was already there. So, we didn't have issues to the extreme that you're having them... but we still had them.

One thing that helped at that stage was to discuss the idea of rights and privileges. Sometimes we granted DD privileges, which she enjoyed, but we could take away at any time. She earned them through good behavior. For particularly good behavior, extra rewards were often done... trip to the park, beach, etc.

For misbehavior, she lost privileges. At three, losing bedtime stories was the default punishment, because that was something she cared very deeply about. Late at night, well after the issue had passed, she'd ask for her stories, as if nothing had happened. This was another test, so it was no time to bend... no stories means no stories.

Another test she liked to do was the something-now-for-something-later deal. For instance, she might ask to stay up a half hour later, and offer up her stories in exchange. Since I would have been reading to her for over half an hour, this still gets her to bed on time, so it's a deal I'd accept. Then I'd put her to bed, and she'd demand her stories. No dice.

Apart from privileges, we explained how she enjoyed rights, things that her parents absolutely could not take away from her at all. This became a useful background for explaining those things for which we simply could not negotiate. "I'm sorry, you can't stay up all night, because we're getting up early tomorrow, and you have a right to good health and a good education, and sleep is an important part of both of those." This framed things in terms of "it's for your own good" in ways she could understand. It was very interesting to watch DD realize that these things were born of something other than our dictatorial whims.

Also, it led to one of the creepiest fascinations for a 3yo, because she wanted to know all about prison.