Update:
This morning after my daughter left for school, I left a short note on her bed telling her how much I cared about her and why I really would like her to give counseling a try. She is not a good verbal communicator and gets uncomfortable in one on one conversations about "serious" subjects, so I thought writing a letter to her might work better. I also printed out a little vignette I found on the Internet about a girl who goes for family therapy and her experience there. So I left these on her bed and then talked to her tonight after dinner about whether she had read them. She had and didn't really want to talk about them, except to tell me she was not the girl in the vignette, but she seemed more comfortable with the idea of counseling and not as resistant anymore. She is planning to go on Thursday and didn't seem hostile/angry about it anymore. So this is a lot of progress! Keeping my fingers crossed that it goes well....