I'm a language teacher, and spend most of my days having one-to-one conversation-based lessons with adults. In the vast majority of my lessons, the atmosphere is a friendly one - since I have to encourage conversation, naturally my students talk about their lives and I end up telling them a little bit about mine too. That said, with 99% of students our friendly relationship starts and ends in the classroom - I never see them outside our lessons. Everyone understands the boundaries.
However, there's one lady who I've been teaching once a week for over a year. She seems to be able to draw no line between our friendly classroom relationship and our "outside" lives. From the start she has been inviting me to do stuff with her outside the lessons. I have always made excuses, but remained friendly in the lessons because I have to keep teaching her and if I were to just say outright "I don't want to be your friend outside these lessons" I think she'd take it very personally and it would be horribly awkward.
Another reason I am reluctant to spell this out to her is that she has had a very hard life, particularly recently - illness, deaths of people close to her - plus some really horrible stuff further back in her past. She has talked very openly about all these things in our lessons, cried on occasion, and of course I've felt compelled to listen, give sympathy etc. I have never invited her to talk about these things, but she does nonetheless, and when she's literally sat there crying next to me, I have felt that saying "I'm sorry it's a bit inappropriate for us to be discussing this" would just be impossible for me to say.
At one point she told me she was organising a big party. And of course, she wanted me to go. Since she invited me to this party over half a year before it was actually due to happen, I couldn't exactly say "sorry I have plans for that day" so just made vague "that sounds nice" noises, thinking that I'd get out of it closer to the time. But she would literally remind me every week, saying how much she wanted me to go, how disappointed she would be if I didn't. In the end, I thought it would be easier to go than not go and then face the fallout in our lessons afterwards. So I just made a brief cameo appearance (with excuses why I couldn't stay for the full party), which she seemed satisfied with.
Anyway, finally we have come to the end of our lessons together. In fact she wanted to rebook, but my company have made an excuse on my behalf (as they know I was starting to find her difficult to deal with) and told her they are obliged to send her a different teacher from hereonout. She immediately contacted me and left a very very long message saying how disappointed she was and how she hoped it wasn't at my request that they're sending someone else, and how she wants us to still be friends and to meet up soon etc etc. She has also since friend-requested me on a social network, but I haven't responded.
I feel very uncomfortable and am not sure how to proceed. On the one hand I really don't want to foster a friendship with this woman, but on the other hand I'd feel like a heartless bitch if I just ignored her calls and emails (of which I feel certain there will be more). The other option would just be to phone or email her and tell her "I don't want to be friends with you" but I think this would hut her enormously and TBH I'm too much of a chicken to say it.
So what should I do? How should I proceed? Am I being a bitch for having made her think I am her friend and then just blanking her? Or is she being the unreasonable one for not having realised by this point that I don't want to see her when I'm not being paid for it? I feel bad because she is quite a vulnerable person, although seemingly not without other friends and family.
(I posted this earlier but it was pointed out with a little too much identifying detail, so previous thread has been deleted and I've tried to include less detail here. Thank you to those who replied previously - I found the mix of opinions has already given me a lot to think about)