J.,
Welcome to my boat. Both of my boys are different. They are up until at least 11:30-Midnight. My oldest eagerly gets up at 6:50 to get ready for school. (His bus picks him up at 7:15am) My youngest no matter how early or late he goes to bed, requires more than 12 hrs of sleep. He goes to pre-school three days a week and has to be there at 9am. We have some VERY UGLY mornings. My oldest can function on five or less hours of sleep, but my youngest is a major Monster no matter how much sleep he gets. (My husband nicknamed him Monster when he was an infant. Go figure.) I suffer from chronic insomnia so I take three prescriptions to help me sleep. Once I take it, w/in about 1/2 hr I am out like a light.
Here's what works for us. Our boys share a room. There is a TV and DVD player in their room. I settle them in and read about three books, especially ones about a parents love and lots of kisses. (Little Critter books, Kisses by Nanda Roep & Marijke ten Cate, Skippyjon Jones, I love you stinky face.)I put in a DVD, give my boys each a small plastic bowl or sandwich bag of Cheerios and I start the movie. If they are thirsty, they each have a cup of water in the bathroom across the hall that they can go drink. Usually when the movie starts they are engrosed in it and fall asleep. By that time I am out like a light. When my husband gets home from work at about 11:30pm, he wakes me so I can go to bed, turns off the movie, tucks the boys in and all is complete until the next day.
It is difficult when you are tired and running on fumes. My only salvation is the weekends when I don't have to get up at 6:30am. When my oldest was three, we had him in daycare/pre-school with a close friend three days a week so that I could have me time. You may try this, find a preschool in your area, drop him off in the am, take a nap with your daughter for three hours and then go pick him up. DO WHAT EVER IT TAKES TO GET SOME SLEEP, even if it costs $. You deserve it.