Maybe if she learned to work with her curls she would be happier. I know at 13, that is going to be a very difficult thing. My hair got curly at 13 and all I wanted was straight hair too. I gave it up senior year because straightening just about every other day was so much of a pain.
Here is a few things that might help:
If her hair is one length and really thick, get some layers to reduce the bulk.
Never brush curly hair. It pulls out the curl and causes it to frizz up.
Use a diffuser to blow dry because it will gently cup the curls and not blow them around like a regular dryer does.
If she is still adamantly against wearing it curly, then go ahead and get it chemically straightened.
There are downsides to getting hair chemically straightened. It takes awhile just for the roots to grow out. If she doesn't want to get it retouched she'll probably be straightening it every day to get it straight. And if she wants to go curly, the hair may not curl that easily. I've never had it done, but this is just what I've heard. I really wouldn't get it chemically straightened though.
Tell your daughter that many people would kill for her curls and and to check out
www.naturallycurly.com. She'll find many people in the same boat as her.
Once I learned how to take care of my waves and curls, I've only straightened one time.
If she learns to work with her curls, she'll be the envy of her peers. I'm sure they are gorgeous.