I wish I had the answers for you! However, I say accept all of T's help. You are going trough a very journey and need any help possible. Also just because a person has family and loved ones by their side does not mean they have a good support system when it comes to facing death. When my mom was terminally ill most of her family stayed away..she had myself, my husband and my step father. Everybody was too busy in reality it was because they couldn't deal with it.

Your T is there because she wants to not because she has to. She sounds like an amazing source of love and support for you. You deserve to have her in your life. Accept her support without question.