Hey Sun! Now, I don't mean to dig too much, but I'm just trying to help... Does your daughter understand the reasons why it was suggested that she enter therapy? What are the reasons that she gave you that she doesn't want to go?
In answer to your question, most therapists, especially ones that specialize in adolescents are very well equipped to deal with clients who are resistant in treatment. Most do this by "joining" with the client and emphasizing the degree to which they are on the client's side.
I started therapy when I was 17. However, it was my choice because at that time I was already experiencing constant panic attacks. Looking back at my life, and knowing what I know now, I should have (and would have liked to) start therapy a lot earlier than 17. However, that opportunity was never offered to me, and it wasn't recognized at the time maybe I had a problem. So, I think your daughter's really lucky that you are taking such good care of her

Paying attention to the signs of a problem, and planning for treatment before it escalates. But of course, to a 13 year old, she may not see this side of it.
Have you ever spoken to her about what kinds of things you do in therapy? What does she think about you being in therapy? This is a tough situation. It really depends on what the problem is, but if you feel that therapy is a necessary answer to the problem, I think it would be okay for you to insist that she go at first, then let her make the choice of whether she wants to continue. Therapy is one of those things that you can't expect a lot of people to see the benefits and positives of,
until they try it. Sometimes, even then, they don't exactly see the benefits of it, but at least they enjoy going. It's often hard to step outside of the situation and see how it's beneficial. That's something that usually comes down the road!
But in conclusion to my long-winded answer, I think in this situation it's totally appropriate to step in and be the parent, and insist that she go for a bit. It's for her well-being. And of course it depends on the severity of the problem, but if she was sick, you would insist that she go to the doctor, you know what I mean?
Good luck, let us know what happens!!