Well you need to get what you need, but IMO you are shooting yourself in the foot by declaring to potential T's that you have BPD and an unethical T. And at this point I would question the BPD dx cos you're being pretty darn obedient or compliant or something. And "unethical" makes it sound like a sexual r/s, not mutual dog-walking. You could ask a prospective T for a consult, like for help for a referral to another T once they hear your story.

You don't need to take care of this T. She has her sister to look after her if she needs help. She does kinda sound like she's losing it. Maybe you should talk to her sister if you have concerns for her personal safety if you leave her. But I hope the sisters are not coercing you into a financially abusive situation.