P.M.
You are asking a wonderful question, A., and are realizing that you really need some new information about how your daughter functions so you can set a more effective course for the two of you. Lots of parents don't realize how immediate young children are. They are not planners, and rewards that stretch out much beyond a day really don't connect for them in a meaningful way.
I suspect that your rewards chart worked really well at the beginning because the earning of the star itself was the reward that your daughter connected with. She gets a star (kids like stickers) and you are happy. Perfect! The promised future reward is still vague and abstract in her mind. Particularly if it will take more than a day or two of effort to achieve it, and even more so if her stars that she earned can be taken away from her. So whatever interest she had in the larger goal fades – she does not believe in it, because it will never arrive.
Oh, well, may as well have whatever fun we can have now. At least making independent choices is a bit of fun and freedom, even if there are abstract consequences.
The best discipline is immediate, as positive, and and as logically connected as possible to the original misdemeanor. Make a mess? Help clean it up. Push a child? Do something nice for that child. Yell at mommy? Take some quiet time to calm down.
To fail to be loving toward a child is always a mistake. Not that you can't be angry at some things she does; we all have feelings and even parents have buttons that can get pushed. But it's necessary to have your own buttons set back at neutral when you decide what consequences the child should receive – discipline is best delivered with a calm, loving demeanor. You really want your child to know she is unconditionally loved, to trust you and to know what to expect from you, to be able to talk to you about what she is feeling – you will need this strong connection as she becomes more independent.
Depriving a 3yo of play or fun is not a particularly appropriate consequence, if it stretches beyond a very short time span. Deprivation piled on deprivation quickly becomes meaningless. One hour to a child is like a day to an adult. Two days to a child is like a month to an adult. And play is a childen's work; it's how they learn, how they synthesize all their experiences into a meaningful whole.
Your 3yo is doing what a 3yo MUST do, finding out how to be a more independent person. She's in a 2 year period from which she will emerge a much different and more capable person, able to exert some real self-control over her feelings and reactions. She needs your help to get there.
The parents I know who have investigated Positive Parenting, Positive Discipline, Emotion Coaching, and similar terms have had fabulous results, learning not only about their children but about themselves, as well. You can find these and related links in a google search, and some particularly fabulous books that teach these are How to Talk So Kids Will Listen, and Listen So Kids Will Talk, by Faber and Mazlish; Raising an Emotionally Intelligent Child by John Gottman, and a very helpful website called Ask Dr. Sears (here's a page on discipline: http://www.askdrsears.com/html/6/T060100.asp ). A book that you might find particularly meaningful is Playful Parenting, by Lawrence J. Cohen, PhD.
You'll hear from parents who believe in spanking as the cornerstone of good parenting, and they may complain about lenient and permissive parenting that lets kids run wild. Positive discipline is NOT lenient, it must be applied persistently to work (just like spanking), but it simply believes we don't have to strike, overpower, or shame children to make them behave. In my experience, and that of quite a few families I've known, positive parenting results in terrific kids and wonderful family relationships. I hope you will investigate it. And now is the perfect time!