This sounds SOOOOO familiar! I have 2 very willful little girls. As you say, these are usually the smarties! It's not entirely bad, because already they've learned to negotiate from a position of strength... but still, you can't have people under 4' tall running your house.
The only thing that I have found to work is to intervene IMMEDIATELY. (We've been doing this since my oldest was 18 months; she's now 5.5.) Do not give warnings, chances, etc. The moment you see the behavior that needs to stop, tell the child no. (I don't have a ton of rules, but the ones I have are inviolable and the kids know it.) If she does not stop immediately after I've said no, I calmly march her off to her room (we don't keep toys in their rooms, so it's not a lot of fun or anything). Then I tell her, "Since you can't listen, you will need to sit in your room alone. When you're ready to behave like a big girl, you can come out." For my daughters, simply being sent to their room usually sends them into tears. I leave my older daughter there for 5 minutes, my younger one 3 minutes (because she's 3) and then go in and say "We don't say mean things. If you can't say something nice, just be quiet." (or repeat whatever other rule she just broke). I have her repeat it back to me to be sure she understands.
Then the next time I ask her to do something and she does it right away, or when I catch her doing something really helpful or kind, I mention how proud I am of her. Her face lights up, and over the past couple of years her offenses have grown much fewer and farther between.
Now, my youngest (almost 3) is still very much a work in progress. But we're working on it! With younger ones, babyproofing the heck out of your whole house does help. We were having a big problem with our youngest getting into things (lotion, conditioner, vaseline, anything gooey), so we babyproofed all over again and that solved the issue. The fewer rules you have, the more successful your kids can be.
I think the trick is consistency, and intervening right away (rather than giving warnings again and again, which teach them that they can always push you).