There are many things going on in your post, and as it is late I don't have time to respond to all of them, but I will try to hit the major points.
I think your issues are larger than time management between dyad time and tryad time. It sounds like there is a communication gap going on in all of this. I wonder what he is thinking? It seems the two of you are squabbling over his time, and the time between the two of you is not appreciated as quality intimate time.
In my closed tryad it seems we have so very little time together that we don't put up solitary/dyad/tryad time barriers. With a small child, long commutes and three stressful jobs we work hard to just enjoy the time we get together. We would love to all be together all the time, so in a way we are always 'aiming' for tryad time. That said, if two people are together then they try to enjoy it. Like in your situation, my girlfriend and I get more time together than either of us gets with our husband, but that doesn't mean we assign his time to each of us.
Truthfully, I just don't have the energy for that. We work better when we let time be fluid. I think the lack of sex may be a large issue for the three of you too. We try to have sex often, and we regularly sacrifice things like tv for sex. Sex is a healthy relationship glue, in my opinion, and a lack of sex can magnify problems.
I guess I don't quite see if she is really interested in sex with you? She seems to be using confrontation and ranting to avoid sex during her dyad time with you and avoiding tryad time (where presumably she would be having sex with you too) in general. Its not clear to me if she having sex with your husband during their time. Her calling your feelings 'insecurities' is also a distraction. Of course you should be pissed if she is 'checking off a box' by being with you. Isn't she supposed to be in love with you? When you love someone you don't think of spending time with them as a necessary evil.
I think it would be helpful for you to sit down with both of them and communicate your feelings. Maybe have one of those 'talking sticks' so that she can't monopolize the conversation and everyone gets their say.