"You know what? I feel so much better just being able to talk this over with you people! My partner and I are talking about it heaps but it's different because she's involved too."
Oh, I do understand that feeling... I am here because as supportive and open as my husband and our girlfriend are, there are issues I sometimes need to sort out before I can bring them to my loves... and sometimes there are things that I'm upset or anxious over and just talking about it or reading reactions to it makes me realize how insignificant it is, and that I'm overreacting (which I def do sometimes).
I understand not wanting to give up your friendship with T. I think that if you are able to remain firm in the face of temptation, it will work itself out. I do think that sleeping with her before she's resolved her relationship with K (either by allowing it or by that r/ship ending), it will just create a very messy situation. You mentioned that the time she cheated before resulted in her NOT speaking to that person anymore, and that's what I'd remind her and yourself of when the temptation arises, and I'm sure it will given the connection and the amount of time that K will be gone. It sounds like you value the friendship over anything sexual and that is probably the thing that will keep you both strong.
It is good that your partner is getting help... that's definitely important. It's also good that she is supportive of what you are building with T and that her lover is supportive of your family dynamic. I agree with you on the difference between swinging and poly. I could not swing. My best friend and her husband were swingers and I was semi-involved with them sexually before I met my husband (and early on before there was a commitment between him & I), and I always had my doubts about him. I didn't know him well enough... she and I didn't talk for 8 years (not exactly related to that), but I was not even remotely surprised when she told me that one of the women they were with regularly - a friend she trusted - had been having an on-the-side affair with her husband, despite the three of them being sexually involved together. I always got the impression that he would've been happy to get me alone. There were subtle hints, and it made me uncomfortable.
When I told her about our triad, she was telling me that she couldn't imagine that because the emotions would scare her. For me, opening my marriage without that emotional connection would just break my heart. It would taint our marriage... I am *not* judging anyone else's choice. I'm just saying I couldn't go that route. Our GF was a HUGE surprise... but the love is what makes it worth the effort and any risk of getting hurt.