Dear G.,
What a great mom you are, not rushing to the medicine cabinet for a solution!
I would recommend seeing a good Integrative M.D. (deals with traditional and alternative medicine) to see if diet and supplements might make a difference. I see a woman named Sandra Pinkham in Columbus, and my life has changed unbelievably since I started following her advice. If you can't find a good Integrative M.D. in Dayton, it would be worth the drive to Columbus to see Sandy. She doesn't require patients to come in every whip stitch, so you wouldn't have to make the trip often at all. In the 11 months I've been seeing her, I've only gone three times (including my first visit), and two of those were due another condition I had that was unrelated to the insomnia.
When I first went to Sandy, I was doing what I call "sleeping in spurts." For the life of me, I couldn't sleep more than a couple of hours at a time. Sandy recommended melatonin, along with significant dietary changes. The diet worked so well, I never even had to open the bottle of melatonin I bought! I noticed a huge change within the first three days I was following the diet. It's been 11 months now, and I am still sleeping well and feeling good in the mornings. I used to have to take at least one nap in the day time, but now my energy level is so good, I don't nap at all.
If you're interested in Sandy's contact information, please send me a private message, and I'll reply with it.
As someone else mentioned, it could be that your daughter is growing up and doesn't require as much sleep as she used to. At 11 1/2, she's also approaching some major hormonal changes, and that can have an effect on sleep patterns too.
Good luck!