It's really true that if kids don't get noticed for good behavior (be 'caught' doing something good), they'll get attention HOWEVER they can!
If you're telling her to do something 3 times before getting a response, something's already not quite right. My mom (now in heaven) gave me wonderful childrearing advice in one sentence: "Don't say anything to a child unless you mean it." (If you don't intend to enforce it, don't say it; and if you say it, enforce it). Also, never speak to a child as if you're challenging him/her (picture a mom standing with her hands on her hips, head cocked, one eyebrow raised, and mouth set/lips clenched). It may work with some kids, but not many. I've found that the most compliant children can usually be the most beligerent/stubborn when 'ordered around'.
She's 'pushing your buttons', and it sounds as if you need to ignore it as much as possible AFTER telling her -- calmly, but 'in no uncertain terms' -- that this is unacceptable behavior and it will not be tolerated. (Also sounds as if this is a bigger deal to you than it is to her -- you're making it fun for her with your strong reactions. It's REALLY not that big of a deal. I think about every kid goes through a similar phase. She's trying to express that she's not getting enough of the 'right' kind of attention in life [daycare, home]).
Use positive reinforcement. EXPLAIN that if she can go a certain length of time (one hour, one evening, one day, or whatever), she'll get a sticker/star, points toward a reward (such as an ice cream 'date' alone with mom or dad), etc. Ignore the 'ugly' behavior, but be sure to notice if she DOESN'T do it!
P.S. I have 4 grown kids and our oldest daughter has given us 3 little 'grands'. Her 2-yr. old is a very sensitive little boy who's acting 'rebellious' (sounds like your daughter). I told her to 'ask' him to 'help her' by putting his toys away (or whatever she's 'asking' (telling) him to do, then go away as if she EXPECTS him to do it. That usually helps (I'm prone to be that mom with her hands on her hips, and it was hard for me to NOT be! LOL)
Good luck and God bless!