Not to mention the assumptions that Rand's people would all listen to her instead of him. Did she REALLY think she was going to sway people who need him for their people to survive the Last Battle and the mother of his children? Of course the idea of Nynaeve screwing up that bad is ludicrous, but that doesn't mean Egwene isn't going to try.

She assumes her friends will support her, and goes and picks the two friends who by all appearances are closer to Rand than to her. Nynaeve has been spurning Egwene for Rand for months now, and unless the parallels with Siuan & Moiraine are closer than we know, Egwene & Elayne's relationship does not encompass bumping uglies, which does tend to affect which side a person comes down on.