It's obvious that Cadsuane and Sorilea want to teach Rand laughter and tears again. For this reason they brought Tam to Rand (and in the end it worked in a way). I wonder, though, how Cadsuane & Co. could actually know that Tam is with Perrin. They could have learned it from Sulin, but the general consensus seems to be that it's an error that she suddenly stays with Rand in TGS. Maybe the WO with Rand contacted the WO with Perrin and thus learned about it (if they are Dreamers).

Anyway, Cadsuane states in TGS, ch. 44, that "Perrin actually isn't important to our plans", but that "there are people with him [Perrin] who are vital. One in particular."

The one in particular is obviously Tam. However, Cadsuane implies that there are other people with Perrin, who are also vital to Cadsuane's plans. Cadsuna could mean the other Two Rivers folk, but if one of Rand's closest friends, Perrin, isn't important, then one can hardly see why other Two River people - besides Rand's father - would be. One also has to note that Cadsuane states she has "plans" not only this one plan, so she might have another plan besides teaching Rand empathy again.

My idea is that besides Tam, Cadsuane brought Berelain with her from Perrin. Berelain could be vital for another important plan, namely to get an alliance with the Seanchan. After Rand failed, I could see Cadsuane wanting to take it in her own hands. As a descendant of Hawkwing, Berelain could be used as a mediator, maybe eventually even giving Justice to Tuon, if this is Rand's new sword (the Seanchan like gifts, after all).

Of course the weak point might be Min's Viewing of Berelain and "a man in white who will make her fall head over heels."
Most people think that this will be obviously Galad (while I suggested Beslan as an alternative, which would fit with my idea that Berelain will be used as a mediator). But even if the man in white is Galad, Berelain could simply fall in love with him, but leave him nevertheless shortly after this to do her duty (e.g. Egwene and Gawyn were also separated for a long time).

Alternatively Berelain might become a negotiator with the Borderlanders in Far Madding, although for the reason of her ancestry, the Seanchan seem to fit better.