Cognitive therapists would agree that clients come into therapy with both explicitly stated goals and goals which are not explicitly stated. However, we would be slow to label those goals which are not explicitly stated as unconscious. Our view is that they often are conscious, but unstated, or are outside of awareness but easily accessible (what the Freudians would call preconscious).
We would agree that one of the therapists tasks is to discover the clients unspoken goals for therapy. When we talk about working towards clear, mutually agreed upon goals we do not mean that we simply take the client1s initial goals at face value. In addition to taking the clients initial goals seriously, we try to identify goals which have not been expressed explicitly, and we often propose additional goals for therapy which we see as in the clients best interest. We try to end up with a list of clear goals for therapy which both therapist and client are willing to work towards because we believe that working together towards mutually agreed upon goals increases motivation for therapy and minimizes resistance.
When you say that your new immediate goals with Caroline (protection from substance abuse, unsafe sex, and muggings) were not clearly mutually agreed upon goals do you really mean that you were working towards goals which Caroline was unwilling to pursue? I doubt it. It seems to me that if you were to try to impose your goals on her unilaterally, this would be ineffective and it would replicate her relationship with her parents in an unhelpful way. My guess is that you mean that the immediate goals and the long-term goal of working towards a healthy, differentiated life of her own are goals which you proposed and which Caroline agreed to. If that is the case, Cognitive Therapy would consider them to be mutually agreed upon goals. We probably would spell out the goals more explicitly and concretely than you do and we would intervene differently, but I am not sure that the goals of therapy would differ.