Here's what I'll say about Siuan for right now, since their are still a lot of unknowns floating in the air: I think her actions in this episode are largely in accord with her book characterization no matter which way the show breaks on certain details.

Siuan's central character flaw in the books, the thing that largely leads to her downfall, is her default response to most problems being to exert raw force and control. It was how she handled the Hall of the Tower which allowed opposition to coalesces around Eladia and Alviarain, it was how she handled Gawyn creating a resentment in him that would drive him to side against her during the coup, and how she forced Min to remain in the Tower against Min's wishes which was the catalyst for Eladia realizing she could strike against Siuan at all.

And it's what Siuan does in this episode when confronted with a problem she does not have another way to deal with. Moiraine is with holding information from her? Go to Cairhien herself and seize the tiller of events with her own hands. Rand is running wild, derelict in his duty? Take him captive and bring him to the Tower where at least he will be under her eye and safe from the Forsaken. Moiraine is attempting to abscond with him as a result? Cut off her avenue of escape by any means necessary, even if it means damaging her personal relationship with Moiraine, possibly forever.

And that's the other thing to keep in mind: Siuan, like Moiraine, fundamentally does not trust anyone except her partner in conspiracy. She can't. For twenty years she's been on a quest that will lead to her stilling and execution if it is ever discovered. She and Moiraine are each other's confidants and allies, their deepest and most important loves. But even in the books Moiraine is withholding information from Siuan out of a sense of greater good. The difference is that in the show Siuan becomes aware of it in the show and of course she begins to doubt and loose trust in Moiraine as a result.

In her mind she has gone almost at once from being a partner, one half of a team that trusted in and depended on each other, to being on her own against the storm. If Moiraine didn't tell her about being stilled, what else might she be holding back? And if she is stilled, then realistically, how much good can she do for their cause now? How can she keep Rand safe from himself and the Forsaken, prepare him for what's coming, when she might not live another year? And that agony- that pain that the person she trusts and loves most didn't just betray that trust but also might not be around long enough for Siuan to be mad even be mad at her- has to be put aside because the mission, the duty, is everything to Siuan, just like with Moiraine. The stakes are too high for anything else.

So she falls back on the safety net of the Tower's traditions and secret plans. Take Rand to the Tower, keep him safe, prepare him for what's coming and trust to the Light for the rest. Take away his agency for his own good and the good of the world (something it should be noted she's wistful for the ability to do in TSR when she wishes she could keep hiim from a learning a word of the Prophecies, which is the same scene where she outright admits to Min she intends to try and control him in), and bring him firmly under her thumb. And what does Moiraine do? Enlist the aid of one of the Forsaken to break Rand free and flee to Falme through a Waygate, which is at best an INSANELY risky and potentially very stupid play, and at worst tacit confirmation of her worst fear, that Moiraine has gone over to the Shadow, and everything is on the brink of being lost.

And where does that leave Siuan? Isolated and alone and with no other fallback by her same response: to keep exerting raw force, to pressing the spring down until it snaps.