You "loved one" isn't just sabotaging therapy. He is sabotaging everything about you to keep you weak.

I believe you will get better, have more skill at managing your BPD and use what you know about yourself to take control and get as far away from this situation as possible. I think you have the power to do this, as hard and scary as it sounds. I hope you can speed this process up, IMHO that needs to happen for the sake of your child. What is she learning/seeing?

But you need help. Homelessness is not a good option for lots of reasons. You mentioned your mom being a problem too, but if you were to go there, could she do it for your child? Would you be able to work and your mom help with her? Would you be able to shut out the negative she might bring for a time while you work on your independence?
What help do you need exactly? Name them all. Then you can tackle each one in turn.
Safe Shelter
Restraining Order?
Therapy
Work?
Child Care?
Transportation?
Does your T understand how dire your circumstances are? Please consider another T if this one can't get you real help.
My heart goes out to you as you struggle to get out from under this terrible weight.
Please keep posting. Many here care and want you not just to survive, but you and your child to thrive...