It sounds like this has gone from a quickie, let's have a FMF threesome, to more of an actual polyamorous relationship.
You have tried a triad before, which was a failed quad, it seems. So maybe (or maybe not), you realise there are a LOT of relationships in one triad.
You and Tabitha
You and V
V and Tabitha
You and V and Tabitha
You need to make all these relationships easy and nice and loving and free. No one should sit home fuming when the other 2 are together. It sounds like V was fine with you and Tabitha being platonic friends, but as soon as sex came up, he lost his shit. He didn't want you girls to even hang as friends anymore once he had you two doing sex together, even in his mind.
Some triads only have sex as a threesome. That means, even the original couple (if there is one) do not fuck unless the 3rd person is also in the mood. Much more common is doing sex as a twosome, or as a threesome, either being just fine with all 3 partners.
Of course, you and V are used to having sex one on one. How would you feel if Tabitha requested you and he never have sex unless she was also in the bed? That is the restriction V was putting on you and Tabitha having sex as a twosome. Not so nice to contemplate, is it, needing permission, and having permission denied, from another to have sex with the other, even if the reason that person doesn't want sex is because s/he is is ill, or exhausted, or working long hours, or out of town?
It is good you realise your relationship with Tabitha is more of words and fun hanging out, whereas she and V are "white hot" for each other. Does that mean V and Tabitha will want to fuck one on one like bunnies for a NRE year, while you and she are more lukewarm about it? How will you deal with that? What if V prefers white hot NRE sex with Tabitha over old married sex with you?
As someone said upthread, there are a million moving parts and factors that make triads very hard to do.
And now T is so infatuated she can't even imagine wanting another partner in her life besides you and the man she is hot for. Well, welcome to NRE. Once the original fire banks down a little, she well may find herself getting attracted to another woman or man who is single and has more time for her, with less complications.
Just some things to think about!