An alliance of convenience that the qunari would happily have dispensed of had the Dragon's Breath plan work.
That we know of. I find it unlikely that the Viddasala is able to run such a large operation if she was only a "rogue agent." She literally had hundreds of other qunari in multiple countries working for her, both actual qunari and viddathari.
Iron Bull's standing orders was to work with the Inquisition, until a superior ordered him otherwise. Had he died along with the Inquisitor, his sacrifice would have been a necessity for the Qun.
And yet, this "rogue agent" seems capable of intercepting messages between the triumverate and Josephine.
A necessity. The qunari are unhappy about most aspects of the Dragon's Breath operation, but it is the only way to defeat the agents of Fen'Harel — who themselves command considerable magic — and bring order to the south.
Again, a necessity to combat the agents of Fen'Harel and prevent the destruction of the Veil.
A partial recipe contingent on leeching poison from a high dragon. Whoop-de-fricking-do.
Besides, he attacks you at the point BEFORE you acquire that partial recipe. So that makes perfect sense.
But Hissrad doesn't know that, nor that the Qunari wanted to discard it.
We know Hissrad did not receive word because then he either would not have been there as an ally, or he would have acted like one until they found the first group of Ben-Hassrath, at which point he would have attacked the Inquisitor. Viddasala was the top "commander" of her division. The only one over her was the Ariqun, who was in Par Vollen. She was a very powerful individual. She was like the Loghain of Trespasser. Lower ranking grunts would follow her orders without a second thought.
But if the plan was to kill the Inquisitor, then his superior would have given him the order to do so. In which case, the Ben-Hassrath under Viddasala would have been ordered not to attack Hissrad. Leaving Hissrad in the dark on purpose only causes a loyal Qunari to kill other loyal Qunari. That is wasted life. That makes no sense under the Qun.
No, she failed to intercept Josephine's message to the Triumvirate. She only intercepted Hissrad's, and then intercepted the Triumvirate's REPLY to Josephine. This shows that Viddasala was working against the Triumvirate, and was able to get to Hissrad's contacts. But she hadn't anticipated Josephine having connections of her own.
Again, Hissrad didn't know that, even if it had been true. And I doubt the Qunari would allow the use of magic portals simply to stage a surprise attack on one target that already had infiltrators anyway. Besides, the other targets didn't have eluvians. Viddasala had to send a few assassins and gaatlok the old fashioned way. So the eluvians were never needed to attack the southern nations. Viddasala was using it as a means of travel between the Library and the Darvaarad. A huge no no under the Qun.
Viddasala's notes can be found in the Library. She actually had to reassure her Ben-Hassrath that her commands were consistent with the Qun. Even they began to doubt her when she proposed using Saarebas in some kind of "constructive" way. She was buying into everything she had observed in the Library. A Library full of "demons". No way the Triumvirate signs off on that. If anything, they only would have authorized her to kill Solas, and focus only on him. The Triumvirate also would have informed the Inquisition of Solas' antics and worked with the Inquisitor to stop him. Hissrad would be able to confirm that Solas was acting without the Inquisition's knowledge or approval. Also, Viddasala didn't know that Solas planned to destroy the Veil.
The gaatlok recipe is sacred. The DA2 Arishok states that it would be a Qunari's obligation to die defending the recipe if needed. Viddasala just has it out where anyone can see it while the Inquisitor is attacking the stronghold.
Now, if Viddasala had given Hissrad the order, and he called her Tal-Vashoth in return, only to have her explain that the gaatlok recipe was over there and that Hissrad must protect the secret, THEN Hissrad attacking the Inquisitor would make some sense. But as it stands, Hissrad didn't know the gaatlock recipe was a few yards away. So his choice doesn't make sense at all.