This topic always brings back so many memories for me.
I wasn't allowed to shave my legs, as my DMum decided that shaving was bad, that she was stuck in a shaving cycle and she wished she'd waxed from day one. So she decided, for me, that I should wax. I am olive-ish skinned and have very dark hair and thick hair on my legs (and arms, but I wont go into THAT) and the thought that I would have to wait three weeks minimum to be hairless was awful, let alone the fact that waxing hurt.
Our secondary school insisted girls wore bare legs and ankle socks in the months after easter, so for three months of the year I'd hate hate hate going to school. PE was gymslips, all year round, and I only signed up for Hockey as I could cover most of my legs with shinpads and hockey socks. In winter, i'd wear two pairs of opaques at a time to stop the hair poking through.
Within a couple of years, I took to doing it by stealth. I ended up wrecking my legs, pretty much, as no-one showed me what to do, how to do it safely, with creams etc. I really wish that my DMum had appreciated how much I hated my hairy legs and helped me feel confident about myself.
I got so into the habit of covering up, year round, that I still find it hard to bare my legs, even though I obviously can now keep them hair-free.
I know this isn't a massively helpful post, but please please help your DD by seeing it from her point of view. She obviously feels very self-concious, hence the tights in swealtering weather, and something as simple as Veet, or learning how to shave well will help.