So, did you actually see the psychiatrist? I wasn't sure what you meant by "uncooperative"-- if you actually ended up going or not.
You have the right to be mad at your dad! Geez, you are admitting that you have a problem with lying and then your dad lied to you.

That's not cool. Not only should he have told you the truth about where he was taking you, but he really should have consulted with you beforehand.
However, it does sound like your dad is really concerned and scared, too. He was probably afraid of what your reaction would be, so he figured it would be easier to do it in the manner in which he did.
Think about it this way-- if you tell your dad that you are willing to be cooperative because you realized that you really do need a psychiatrist, it really won't be any surprise to him-- he obviously knows that you are in need of help because he brought you there to begin with! If you are ashamed of being uncooperative and then coming to the realization that you do need help, I can understand that-- because now you have to admit it to someone else... but that is the first step towards recovery. I don't think there is any one of us on this board who didn't go through a period where we were resistant to admitting we need help. It is a very difficult thing to do.