First, I agree with the poster who said get a second opinion--preferably hers. For instance, when I first started showing signs, my dad told me he was convinced I had aspergers syndrome. It led me to do my own research and it was then that I diagnosed myself with spd. As for aspergers...I only met one or two of the criteria but most of the symptoms were definitely not me.
The thing with my dad is, he wants me to be great. I'm what I guess you could say the "brainiest" and most talented of his children. There's a positive side to aspergers in which the person affected is really brilliant and has a great mind. There is no positive side to schizoid, so when I told him my findings, he didn't want to accept it.

I don't know if this applies to your daughter or not, but I, for one, hate it when my parents try to lecture me when I'm preoccupied. My mom will come along while I'm reading and try to ask me how my day went and start a conversation and not understand why I blow up at her. One thing that works with my dad and I is scheduling certain times of days where we can go for a drive or go hiking and just talk. Make sure it's something your daughter enjoys doing (for me hiking) or she'll lose interest.
Another thing that works for me is writing letters. The written word comes more easily to me than speaking, so I prefer it. Don't push yourself on her. Stand back and give her room or she will only draw further away. At the same time, let her know you're there when she needs you.
I'm no expert--I'm only 19 myself--but this is, in any case, what works for me. I read in my research that schizoids often have one friend or family member that they are close to. For me that is my dad. You may or may not be that person for your daughter. The important thing is not to try to be that, but just be there when she needs you and try not to be offended if she pushes you away. Just go away and come back a little later.
You'll probably find it's like treading on eggshells and it won't get any easier as you go on, in fact it will be very discouraging for everyone in the family. All I can say is hang in there and if it blows up, let it settle and then keep going.