I agree with Kitty....I think you should be able to rely on your family T's support. I think it was a positive way to cope with Sui thoughts to call her. What if she weren't officially a T, but just someone who supported you? Your T certainly doesn't mind you reaching out for support from your loved ones, right? Because he knows he can't be there for you 24/7 so you need to rely on others, and it is a blessing that you can.

You said that your T said "you can't have dual therapy relationships"...
but it doesn't seem like the relationship with your family member as a "therapy relationship". You don't go see her 1-2x per week and talk about your problems, do you? You seek her out when you need extra support and understanding. I do the same thing with my H (although he is probably not nearly as helpful as your family T)

I'm sure you and your T will work out a good solution.