I've only skimmed and read the OP's posts, and I may also be projecting, but I feel sorry for your daughter. Her hair sounds like mine. If you brush it (a mission in itself) it looks wavy. It isn't, it's curly.
I spent my childhood and teen years HATING my hair. Even at age 10 I remember my friend telling me I should put water on my hair to smooth it down so it would be shiny and glossy like hers 
My friends during my teens had long silky hair that was easily brushed that they wore down all the time. I only ever wore ponytails and buns. I never felt pretty as a teenager.
As an adult I have discovered the curly girl method and my hair is stunning. Yeah I'm bragging, but I hated my hair for nearly 30 years, I've earned some bragging rights!
Also, it's easier to deal with now. 2-3 washes a week and each morning I get up and go, no real hair maintenance required.
Do not treat her hair as if it's straight or try to make it straight, try to discover what her hair is naturally like and go from there. There's websites dedicated to curly hair, get her looking online for hair tips.
Oh and if a hairdresser offers to thin her hair using thinning shears or razors, don't do it! It's the worst thing to do for curly hair!! The thought makes me feel a bit sick...