My advisor wants me to mentor a difficult peer
I'm in a US PhD program in a small research group (5). My advisor is coming up to retirement and only has me and this other student left in the earlier stages of our PhDs. Let's call her Zoe. Zoe is a year behind me but a few years older as she had a different career before going to college and graduate school. She is extremely fragile and has a lot of mental health issues, which I am of course sympathetic to. However, her issues are beginning to impact everyone else in our research group, but primarily me. I came into the program relatively young but with a lot of experience in both research and teaching, and so I was made the Head TA for another professor in our department almost immediately after I started. I've successfully run that other professor's classes for 2 years now. I didn't teach for my advisor because he didn't have enough TA spots the semester I started teaching. This fall, Zoe starts her teaching requirements. Her attendance is very patchy, even for her own classes. At one point she was too depressed to come in person for a month, so my advisor has preemptively given her a really straightforward teaching assignment in the fall, which is being a co-thesis advisor to a senior student.
He then asked me if I would drop the class I TA for in the spring so I could TA the same class as Zoe so she could have a mentor. I was completely taken aback and shocked and I refused because our other professor is relying on me and I love the other class. He explained that he didn't want Zoe to be alone and needed her to be mentored when she teaches his spring class as it's of course bigger than the thesis advising one. I said I was very sorry but I wouldn't do it as I had already committed and so he said he was going to see if he could find another student to TA alongside her and basically cover for her if/when she gets depressed. He didn't state that out loud but that was the implication. He seemed shocked when I said no and was a bit grumpy with me for a few days afterwards.
Aside from this, he wants her to come to other TAs' fall classes and shadow us so she can learn how to be a good TA. He has not done this for any other student. I should add that Zoe is not a particularly nice person. I told her that I didn't like physical touch and she quietly said to me she would 'keep hugging me until I liked it', which was super creepy and weird. She now makes a show of hugging me in front of our advisor so it's difficult for me to say no. He has changed group meeting times for her, and walks on eggshells around her and expects us to as well. She regularly comes to lab or group meetings crying or sullen and is also adversarial in research discussions and tries to talk down to us.
Even in my own advising meetings, my advisor brings up Zoe and her problems and asks for my advice on them. He does this to everyone but with a dwindling research group, a lot of it seems to fall to me. I am very avoidant of her but he is trying to force more contact. He seems either fond or scared of upsetting her but it is driving a wedge between everyone else. Does anyone have any advice on how I can speak to him, or at least avoid Zoe as much as possible?