Parker, I think RVP's little princess sounds more than a handful for a 4 year old. Like when I was 4, I drew on the walls in pen so it was harder for ma to scrub off. I would climb to high places like the top of a book shelf, just to test their reaction. I would scream in public places just to get attention. At 7 my first computer shut me up. I was on that little mac literally day and night on kid pix, prince of persia, writing stories etc.
RVP, I pride myself in turning little ones into cherubs. You need to speak her language. You've got to look her in the eye and be honest. Treat her like a mini adult, with respect. Set boundaries and keep your side of the bargain. Like, if you draw me a Picasso replica I will tell you a funny story. Don't get her to draw anything, get her to bring out her best drawing skills. Make her do her best in EVERYTHING. It'll take her longer and she'll develop a discipline to be patient and less stir crazy. She sounds like a perfectionist, channel that.