He's been selected to infiltrate Elayne's inner circle, in order to eventually kill her, or so he thinks. It wasn't to happen soon - Elayne had been promised to her as Queen, possibly a slip by Shiaine but Hanlon long thought the Shadow's plans involved putting Elayne on the throne, and he might be right, or not, in that.

It's not Moridin who sent him to Shiaine, he had Moghedien find him and order him to seek Shiaine and follow her orders. When he gets there, Hanlon is confused a bit, because Shiaine tells him she asked The Great Master Moridin to send him a man with brains. He's never heard of any Moridin (the great master is what revealed to him Shiaine was involved with a Chosen, or claimed to be... he never heard of any Moridin, and thinks "who in the Pit of Doom is Moridin?", then thinks it doesn't matter, he got his orders straight from the GM Moghedien herself, and that was enough for him.

Incidentally, this happens pretty much at the same time the murder of Ispan by Careane was carried out (same chapter), and many believe Moridin ordered Moghedien to clean up her own mess.

So yeah, Moridin has involved Moghedien in his Caemlyn plot around Elayne before. It's proven with Hanlon, and quite possible with other things. Moghedien's the one who knows Elayne is in love with Rand, notably, and Shiaine pretty much freaked out when for a second she wondered if there was any truth to the rumour Hanlon was the father of Elayne's babies. Apparently, Shiaine has orders to make sure Hanlon doesn't touch Elayne, and to report anything she hears about the father of Elayne's babies... It sounds to me like Moridin wants to make sure Moghedien's right, and Elayne didn't ditch Rand and took another lover since (how she publicly rejected Rand would make him suspicious). She might be a lot less interesting to Moridin if she's ditched Rand - she was certainly not worth the convoluted plot with Shiaine, if that's the case. At face value, Shiaine's plot is still making no sense at all anyway... the way Hanlon was infiltrated was so inept Elayne figured it all out right away, and it doesn't make sense Moridin would think otherwise... and the way Shiaine handled Hanlon almost garanteed Hanlon would lead Elayne to her eventually... so what Moridin is really up to in Caemlyn with his bunch of inept buffoons is still very much a mystery.

In any case, as I said earlier, Moridin has in Moghedien an Elayne expert who also knows part of Mat's entourage (she was in Salidar), and Cyndane knows Perrin. We know the two women have been spotted by Graendal's spies involved with Moridin's orders to kill Mat and Perrin. It seems extremely logical to me to believe Moridin chose Moghedien to handle Mat who was heading for Andor, and Cyndane to handle Perrin. He would be a bit dumb to send Moghedien into the woods after Perrin when she's been involved with Mat's entourage in Salidar (Thom, Juilin, they were both there, and Elayne, Birgitte were also part of Mat's entourage in Ebou Dar), when Cyndane can't be trusted around Elayne (unless the idea is for Cyndane to go beserk and kill Elayne... in which case she'd have been suitable enough, but that appears not to be in Moridin's plans).

So, again, I'm pretty sure it's Cyndane-Perrin, and Moghedien-Mat.

Moghedien the devious in the shadows makes a more interesting foes for Mat than sub-Lanfear. Perrin's pretty much the one with problems with too pretty women, beside. When you already have Berelain to bear with, what's a bit of sub-Lanfear to add to the mix. (Incidentally, Berelain is known to Lanfear, who used her as messenger once. One more element to suspect it's Cyndane who's closing on Perrin, and Berelain could even be someone she tries to use eventually).