She got deposed before he ever got going. She wanted to be in control of him, and was in agreement with the Reds on that issue. In fact she was surprised, because she automatically thinks of them as the enemy and expects them to oppose anything she wants (unlike Rand, who was willing to entertain the idea that they could be brought around), before she realized that her position was a logical one for the Red Ajah.

She was deposed for keeping secrets from the Hall, NOT for failure to get control of Rand, or if that was a charge, that was one of the laughable ones the Salidar group thought were unjust (because they could not conceive of letting Rand run free either, and did not believe it of Siuan).

In Fal Dara Moiraine kept things from her because she mistrusted Siuan's judgment, claiming that she could not accept the necessary damage and losses ("The world will burn no matter what we do - Siuan could never see that" - or something to that effect) that would come with the Dragon Reborn. Moiraine had to duck away from Siuan in order to go study with Vandene & Adeleas, and had to present her less-control plan to Siuan as a fait accompli.

Siuan was the one who was appalled at Rand going after Callandor because she KNEW the man she hadn't seen in an entire year was "not ready yet!" Siuan was the one figuring out where Rand had disappeared to after Tear, and telling the other Aes Sedai about it so they could get their hooks back into him. She was the one who apparently had a running argument going with Nynaeve and Elayne over how trustworthy he was. She was the one who said "We can't let him get too powerful" because then he might not need the Aes Sedai. To Siuan, Aes Sedai being in control was more important than the Dragon Reborn having the power to do what he needed to. She was the one who tried to have Min spy on Rand and report to her secret agents.

Don't dare try to argue that Siuan wanted anything other than to control Rand. No matter how benevolent or selfless her motivation, she still wanted the same thing as Elaida and every other Aes Sedai (or at least those who sat on their asses in the Tower with their heads in the sand, only venturing into the real world to dablle their fingers in national affairs and screw up ordinary people's lives by withholding protection from bandits or flooding rivers and messing up the weather). Her insane departures from normal practices and willingness to endanger "girls" to whom she had a responsibility to protect and train properly was motivated because the Black Ajah scared her a lot when she first was raised to the shawl, and she got a deer-in-the-headlights mindset towards them.