Try using picks instead of a brush. My daughter's hair is Shirley Temple curly and so thick we can barely get a large hair tie around it. She used to pitch a fit too.
Get her up earlier and let her work the worst of it out herself. Give her a spray bottle with water and a detangling spray. Also, look at the fructis (I am not getting up to look at the spelling of THAT, lol) products. Get the spray curling gel. I have curly hair too, it is just not that thick. I either use the gel after the shower or spritz my hair with water and then the gel, then you scrunch and go. The only time I ever use a brush on mine is if I am putting it in a hair tie, otherwise, I don't even pick it when I get out of the tub, just shake it out and srunch it.
Also, my daughter has found that it makes a huge difference what shampoo she uses. One for getting curls under control.
In an effort to not get up and look at the daughter's hair care products, I came across this website that might be helpful to you. http://www.naturallycurly.com/about-us
Now that I am no longer lazy, my daughter uses Pantene Hydrating Curls Shampoo and Conditioner, Pantene Extra Straight, Paul Mitchell Super Skinny Serum, Biosilk Silk Therapy Conditioner, Neutrogena T/Gel (if your daughter's skalp dries out), and a couple of others. Some products she likes better than others, some she uses when she knows she is going to try to straighten it, and hair just needs something different occasionally to stop product build-up.
One thing I would recommend is hightailing it to Hulen Mall and buying one of the hair straighteners from Italy, one of the kiosks on the lower level near Macy's. I don't remember how much it was, but it was cheaper than many you would buy at the beauty supply and was unbelievably effective. Made of porcelain I think and kept at a lower temp so it does not fry your hair. Even if she appreciates her hair and leaves it curl most of the time, she will occasionally want to straighten it and it would be an excellent investment.