Welcome to our forum.
It sounds to me like things are moving in a positive direction for you guys. How is "T" handling the jealousy so far? My main advice would be to take it slow, baby steps, checking in often with "T" to find out how she's doing. Actually periodic three-person sit-downs with you, "T," and "K," would be a good idea.
It would probably be reassuring to "T" to know of how important she is to you, so be sure to remind her about that from time to time. And as I said, take it slow, easy does'r.
I am glad you could join our site, and hope it proves helpful to you in forming your new relationship.
Love means never having to say, "Put down that meat cleaver!"