That we all have the same goal, that being to repair the contact between D and myself. Yet, whilst I have shown patience and willingness to find solutions by slowly restoring contact,

Has your daughter articulated that she shares this goal? I guess I don't hear much room in your account for your daughter's feelings, probably anger, to be expressed. I don't think her mother taking her to therapy, and taking her home, is unusual or controlling. I assume she is not part of the sessions? But as the T seems to report to you, I assume she also reports to the mother. Even to me just reading on-line, it seems that your D has been made, despite any good intentions to the contrary, the "identified problem." Not surprising that a teen in such a situation isn't forthcoming.