There really are several things possibly going on here and I will be interested to get your feelings about the AD/HD site - I'll explain why a bit later.
First, its not unusual for kids to not know how to express anger or feelings. Thus, if they can be given ways to do so, then that helps eliminate the sitting and crying forever. There is a whole set of books in the Emotional Impact series that are aimed at this age group. Go here to check them out. http://www.amazon.com/Dont-Rant-Rave-Wednesdays-Anger-Control/dp/0933849540/ref=pd_sim_b_1
And, if you scroll down the page you will find 7 or 8 other good titles. These books should be read with the child and the ideas in the books should be practiced. Which leads to what to do when she gets upset. First, let her cry or scream or whatever. Ignore it completely. If possible have her go to her room and tell her that as soon as she is finished - she can rejoin everybody. Do not try and talk or reason with her when she is upset! Once she calms down, then ask if there is any other way she could have handled the situation and then practice a couple of the ways you have read about. And, when she does get upset and does use some of the books ideas - make sure you reward her.
You are trying to change a learned behavior here. It will take time. So its important to be very consistent - which means that all the adults will have to buy into this. In terms of discipline a very good book is called Love and Logic by Fay and Cline. It would be for the adults to read.
Finally, I am worried about her having troubles at school. By the way, the fact that she is not having melt downs at school is a good thing. I am pretty sure the schools discipline her. The fact that she melts down around you guys and not at school is probably because she has learned what works with you and what won't work at school - which means she has a certain degree of control.
Anyway, at her age - which is old for third grade - she should be doing much better. And I think (heck, I know) its important to figure out why. She does show symptoms of ADD. If she has ADD, she would find learning difficult. Furthermore, things like Anxiety and Depression are very common coexisting disorders due to how ADD effects the childs self confidence. In fact, in " "The ADD/ ADHD Answer book," by Susan Ashley on page 53 she says that 60 % of the kids have learning problems. 25 to 30% have Anxiety Disorder and 10 to 30% have Depression. And if she does have ADD, all of those things are just going to get worse.
I would make a formal request in writing for the school to have her evaluated for a 504 plan. Once again, Ashleys book has a lot of good info on what a 504 plan is and what should be in it. Since the book only costs about $10 through Amazon - its probably worth getting. A 504 plan will help her in school, if they can also figure out why she is having the problems she is having.
I think it might be a good idea to ask her doctor for a referral to someone who can do some testing for ADD. As I said you need to figure out what is going on. All the behavioral change things I have mentioned will help, but there is the possibility that what she is doing is not just because she is "spoiled". I just noticed that you have found a good child psychologist in your area. That probably would be a good place to start for some ADD testing.
Lots of stuff to think about. Feel free to ask questions about any of it! I also am the CL on the ADHD forum here - http://www.medhelp.org/forums/ADD---ADHD/show/175 feel
free to post to me over there too. Best wishes.