Miss Charlotte,
I am caught between two ts too. One my T that I surrendered to take care of my son for suicidality and major depression, and who I miss wholeheartedly. The other, a new T I have worked with since about October. This is a complex issue, but I think what mitigates it in your case is that this woman is a family member. You can have strong, good relationships with family members and the fact that this woman is a therapist by profession should not bar you from this. I think your actual therapist needs to understand you have a strong, close relationship with this woman who happens to be a therapist, and learn to deal with it. She has clearly advised you on pursuing therapy with someone and encouraged you on your therapy path. That you feel close, comfortable and grateful to this woman is important-- that you called her to talk about suicidal ideation is not that uncommon. Lots of people talk to a family member or close friend before they inform a therapist. But maybe your current T was upset that you didn't talk to him first. That does deserve some discussion and thought.
These dual relationships can be complicated. I am working hard to figure how I fit in the this new dynamic of feeling incredibly close to my old T while working with the other one, but the old T isn't my relative, and my new T will have to get used to the fact that I still have all these feelings and trust built with old T. He is also extremely careful to not get in the way of my process with this new T, so we all do what we can.
So my 2 cents-- people's lives are complicated, and therapists are used to navigating through complex relationships with others. It doesn't sound as though your dear relative is interfering in your T process, and it does sound as though your T needs to accept this woman as a supportive and wonderful factor in your life.

Kkins9