She dounds like a pretty typical kid to me. I mean, she's 3, for heaven's sake. Can you even remember what that felt like? I find it helps to talk to my mom about wht *I* was like at that age - gives me a little perspective.
This is a great opportunity to start a discussion about feelings. Kids this age may only know the words for "happy" and "sad" but they can FEEL frustration, anger, embarrassment, shame, and the sooner they understand those concepts, the easier it will be to express themselves.
I personally don't believe that withholding love and affection (like timeouts - or go to your room until you stop crying) are appropriate reactions. Now, if YOU get so frustrated that you're losing YOUR patience, then by all means leave the room. (I CERTAINLY know that feeling, and I'm sad to say I haven't always been wise enough to do it.)But if you can either hold her, talk about the emotions, or just stay near her while she's upset it will help her feel more secure. I had a song called "It's Alright to Cry" that I sang to my boy when he was 2 or 3 and got upset over things. Soon after, whenever he would get upset, he would plead through his tears "Mommy, sing the crying song" (It was from a record I had as a kid "Free to Be, You and Me" - more powerful because it was sung by a deep-voiced macho football player)
"It's all right to cry
Crying gets the sad out of you
It's all right to cry
It might make you feel better
Raindrops from your eyes
Washing all the mad out of you
Raindrops from your eyes
It's gonna make you feel better"
Etc - if you're interested, it's here:
http://www.stlyrics.com/lyrics/freetobeyouandme/itsallrig...
And then I talked about how crying really DOES help you feel better and that EVERYONE cries sometimes, even grownups, even GRANDADS (the ultimate grownup). And that when you cry, some of the hurt and pain come right out in the tears (which is a simplified version of what has been scientifically validated.) And everybody knows how much worse it is when you stifle your emotions and bottle them up. You just delay and build until there's a volcanic eruption.
I have a boy who is almost 5 now - smart as a whip, stubborn as a mule, but very sensitive. And it tends to go hand-in-hand with empathy - kids who are easily upset tend to also be the first ones to notice when other children (or animals) are hurting, too. So that's the positive flip side. The children with the most fragile egos are often the most caring, and that is a wonderful trait to nurture.
About a year or two ago, my son would absolutley crumble into a mass of tearful misery at the smallest setbacks or the slightest reprimand. Sometimes he did better when we gave him a little time to be alone (NOT a timeout, just let him go to a favorite chair in the next room), or sometimes we would sit with him (holding or rocking him, or just sitting close by.) Sometimes we could talk about the feelings, and sometimes he just wanted quiet company.
Then later, he went through a phase I called the "Angry Young Man" - and I have to admit it was a LOT harder to see that he was hurting just as much when he was angry as when he was going through the crying phase. I wasn't nearly as good at keeping patient and calm, either, but I gradually figured out that the same kinds of things were triggering the outbursts, and then I dawned on me that he was hurting just as much inside, it was just that the outward appearance was different - he was displaying anger and hostility instead of sadness. (Maybe he learned from other kids that it wasn't good to be a "crybaby" - so he turned it into a "tough guy" act.) Let me tell you - I much preferred the sad kid to the angry one. It's hard to sympathize with someone who's acting mean and angry.
Lately, he still gets upset sometimes over the SMALLEST things - (it's amazing what will set off an hour-long moping session.) But, I usually don't even notice at first, and then I realize he has disappeared into another room and is either sulking or silently crying to himself. If he's upset over me reprimanding him, he'll apoligise over and over, until I feel obliged to say "It's OK, hon. It was just a little spilled milk (or whatever). It's already fixed. Everyone has accidents and makes mistakes sometimes." (And still he sometimes continues to be upset for another 30 minutes or so.)
Kids this age have their own logic which often makes NO SENSE to us, so it's really hard for them to understand what is a "good reason" or "bad reason" (or "no reason") to be upset. They just know that they ARE upset and often can't control the downward spiral. And they have no conept of what is "over-reacting".
So my theory is that you can only do so much to help them through the rocky emotions going on inside. It's basically just emotional maturity and I think the only thing that can really help is "the gift of time".
You might be able to influence HOW they display those emotions, but I would try to get your kid to talk about those feelings rather than just trying to shut them off. And there's the possibility that if you try to discourage the "crybaby" - you might end up with an "Angry Young Lady". I guess it could happen no matter what you do, but we can hope.
Yadda yadda yadda - sorry to go on so long. It's just been an ongoing issue in our home, so we've had lots and lots of time to think about it and try different things. Don't shut them out - don't try to turn it off. Hold them and let the tears get the sad out.
(I really liked Charlotte's response. How sad and awful would it be if Emily Dickinson's parents insisted on "toughening her up"?)