You meant Ingtar. Sorilea doesn't have an Ingtar-like personality. She's the type who believes mountains will move if she wants it, not quite the type to despair.

She tried to influence Rand in that direction? She has barely interacted with him at all. Since Amys won their argument over leadership, Sorilea has taken a fairly low profile about Rand. And all Sorilea has done so far keeps the Aiel close to Rand. A DF siding with the Shadow would IMO do the opposite, try to split Rand and the Aiel and count on the DO to save them.... It a prophecy "of the Light" that says only a remnant will survive.

Most of what Sorilea has done so far wasn't suspicious. Even in the Verin-Cadsuane-Sorilea episode quoted by Darius, it wasn't Sorilea Verin had doubts about, it's Cadsuane she was testing. She brought doubts over Sorilea's motives so Cadsuane would explain her own goals. It didn't work, and it's only in Far Madding she finally managed to make her talk.

The only thing slightly bizarre on he surface about Sorilea is her deal with Cadsuane. Sorilea like Cadsuane was perfectly aware of Rand's "issues" and similarly worried about them. That's all well and good, but Cadsuane worked overtime toward these goals, while for all their "water pact", Sorilea has in all appearances done absolutely nothing. The WO have long stopped even trying to be near Rand (though it's not really surprising given that Sorilea's the one who told Cadsuane she ought to convince Rand she had no interest in him to make him come to her. The WO have merely been following that strategy for a long time, forcing Rand to call them to help).

However, this may well be deceptive. It appears Sorilea/the WO aren't complacent, and it's through Aviendha the WO work to get Rand to "know his people" and "learn laughters and tears", and it's no coincidence they are so "friendly" to women close to Rand, and so encouraging to friendship between Aviendha and them (they made sure she had enough time to make her first-sister out of Elayne, they were not "indulging her" at all.) There's more than a little calculation behind this, and the same with Min. Even with Egwene, initially. Everything that brings "Rand's women" closer to the Aiel was favoured and encouraged.

That's the part Sorilea won't share with Cadsuane. Cadsuane believed Rand's hardness/darkness was a global threat, and while Sorilea wouldn't disagree at all, she also cares that this problem is solved in a way that serve the Aiel interests, by making Rand care for them as his own people, his own blood (that's little different from the way the WO have codified war among the clans. They let enough feuds and killings go on to hone the warriors, but there's so many limitations it's almost war-games rather than real war, and they have strict control over which men they let become Chiefs - Rand is the exception). The WO already have their solution in mind: Rand will marry Aviendha (and they'll encourage her to get pregnant soon, I bet). This involved encouraging Aviendha to befriend Elayne, to make an ally of Min, and getting Berelain - the woman other women never get along with - gently out of the way and gaining influence over her etc. So the WO are working to make Rand relearn "laughters and tears", their plan is just far better thought of than Cadsuane's.

It appears to me that Sorilea's games with Cadsuane are simply that she realised Cadsuane could be a powerful interference in their plans if she gained influence over Rand, and might see Aviendha as a problem, and may not care one bit about the Aiel. Cadsuane saw this happening already with the way Cadsuane dealt with Min, and she would have been no different with Elayne or Aviendha. Sorilea tested the water to see if Cadsuane would agree with her about Rand's hardness, then made a pact. But she also didn't do much at all to help Cadsuane succeed (beside telling her how to get Rand's attention). In TGS she actually let Cadsuane ruin her own efforts. It's as if Sorilea expected this to happen, half wished it, half wished Cadsuane to be broken. Soon now, Sorilea will resurface to "save the day" with the WO's own solution. Cadsuane's desperate enough that she won't care one bit Rand marries a WO. It's no longer make Rand learn laughters and tears on her own terms, it's anything that might succeed is welcome. Cadsuane wasn't quite there when Sorilea made a pact with her...

I don't think it was even Cadsuane's own idea to bring Tam to Rand. I think the WO suggested this solution to her after her own failure, and they were hoping to succeed. They were testing Rand's ties with his kin, which in turn would tell them how to proceed next. If having Tam around helped and he was open to influence from his dad, this opened the door wide to their solution of marrying Rand to finish turning him around. I think the WO are also quite aware Rand was so far gone they needed to "soften him up" first a bit (now that Aviendha is about to be in the position when she can marry Rand, being a full WO now), or he would flatly refuse to marry the three women and the WO are screwed. No one seemed to want to take the responsability for that attempt... the WO pushed Cadsuane into it, and Cadsuane used Nynaeve. They all knew this could backfire, and they all planned a scapegoat...

Where the WO have a bad case of tunnel vision is that they don't always appear to fully grasp that it's even more vital to the Aiel's own salvation that Rand is the Dragon than the Car'a'carn. It's not a remnant that will survive if the Dragon fails, it's no Aiel at all. Mind you, they have not interfere with Rand being the Dragon, perhaps they just consider they can't be no help to him with that part and must focus on their own prophecies.

The WO who seems to fit the "Ingtar" profile the best might be Melaine (among the top WO characters). She was always the most resistant to Rand, and one might even wonder about her sudden interest to gain influence over a Clan Chief. This might speak of desperation. If she can't sway the WO, she might be able to save her own clan by pushing Bael away from Rand. And IRRC, Bael is becoming one of the chiefs ressenting the way Rand is treating them lately. Aviendha says the WO are working hard to keep the chiefs from turning on Rand (even Rhuarc seems to struggle a bit with Rand lately) but maybe Melaine isn't as dutiful as the others at convincing her husband to stick with Rand.