Having read all the responses over the last days and having read the portion that came from your last thread, I see some stuff that I wanted to point out for you take or leave as you wish;
It seems that all of you are pussy footing around issues and feelings and not being radically honest about what is going on for you. You all seem to have needs that aren't being met because you all don't seem to be willing to put them on the table.
The needs I see here for all of you are as such (and please correct me if I am wrong); you need time with your fiance that is not involved with her and is focused on you, you need him to be present and engaged in you and your relationship so that you can make your own plans and be a strong couple. He needs time with your girlfriend and on his own in order to re-energize, feel like he has a life beyond your illness, and a future that is his; he needs to be a primary to himself. She needs to feel like she is part of your relationship together and that she is needed and wanted at your home and in your lives.
So, if this is the case, is it not possible to sit and divide up time between all of you? Be perfectly honest that this is what you all feel you require to be happy... and then when something isn't about you, you can can know that it comes around to you at 5 pm tomorrow. That way time is divided into chunks that are workable and fair... you can feel happiness with your compersion that they are together and you will have his undivided attention later, because a balance is created. Does that make sense?
I am not convinced that what you have is a triad really. It is in terms of relationship, but not romance. I don't hear of anything that makes me think you and her have an intimate relationship or sharing that doesn't involve him, yet she is involved with him in this way and so are you. Maybe redefining your relationship would help?
I am the hinge of a vee yet the two men that I live with are good friends and help each other out. When shit hits the fan in my life they work together to make things easier for me... one or the other gives up their time with me, looks after our child, takes care of mundane daily routine stuff. They get together and talk, support each other where I am concerned... we are a triad in relationship, but not romantically. Perhaps this is more fitting to what you are in your dynamic.
This really doesn't seem so much about your illness as perhaps you think... it seems to me like a matter of taking the situation, not feeling sorry and bad about it and getting on with organizing time and being radically honest about what is going on...
I wonder why they can't go to her house? Why does she always have to be around. Can't he go there for a few hours, come back and spend a few hours with you and then a few all together? That right there is nine hours of the day... anther three hours he could do something on his own while you and her spend time together. That is a whole day, 12 hours. Maybe planning it out this obviously for a time will shift things and make a natural balance occur.
In my day I spend the morning with my boy and PN until I go to work. In the afternoon after work I spend time with Mono, then I spend time just with my boy, then with the boy and PN, then some time with PN and then time with Mono. The whole day is purposely broken up into chunks of time... somewhere in there I spend time alone or with others... I spend work time connecting with Derby and Leo and often write on here. Such is the nature of my job, luckily...
I hope this has helped. Its a bit scattered. Take it for what it's worth