She sounds like a very spirited kid!
Perhaps the issue at hand is why she is behaving that way to begin with? Are mom and dad really busy and don't give a lot of attention? I can tell you I work about 50 to 60 hours a week and go to school part time while I raise my almost 5 year old on my own. Poor kid gets little good quality time with me, normally just negative attention for the things he does wrong. But for most kids, as long as they get it in some form, they don't care.
To combat his acting out issues, I try (not very successfully, but it helps tremendously when I do this consistently) to spend at least 15 to 20 minutes of Mommy & Matthew time each day. We play a board game, like Chutes and Ladders, or some other game he wants to play, or even just sit on the couch and watch a little TV together while we talk about stuff. His day, his friends at school, the kid is a fountain of information at the end of a day! And then before bed we always brush our teeth at the same time and read a story before lights go out.
Even if you are a stay at home mom, you have to think of your time with her as "real" quality time. Have tea party with her and her stuffed animals. Have her help you bake cookies. Play dress up. Do play dough modeling. If my son wants to do laundry with me, by golly I will hand him the clothes while he dumps them in the washer! It's little things that, over some time (and sometimes even noticed immediately) will help rectify her behavior. Believe me, I KNOW how hard it is to find extra time to really focus, even for 20 minutes, on your kid. You have dinner to cook, laundry to wash, homework, work work, etc, and for the love of god when do I get to relax a little?...you just have to try to give her more of your special mom time and some positive reinforcement too. If she's playing nicely, tell her how happy it makes you when she plays so nice, or says things like please and thank you, or what a good little helper she is. You'll make her feel good because she'll know she has pleased you!
She is only 3...she's not going to stop not listening to you. Just do more to notice when she is behaving, and try to do more with her, give her more positive attention. Good luck!