The Dadric Lords always struck me as a family. A really dysfunctional family whose members undermine each other as often as they cooperate, but a family nontheless. After all, they all have similar heritages, outlooks, powers, and positions. When those facts are taken into consideration with the knowledge that the only real constant companions the Dardric Lords have are each other, then it should not come as a surprise that Azura and Molag Bal can, on occasion, work together.
She also seems quite vain and prideful to me, as she seemed to love being loved, and went extremely nuts when anyone defied her (e.g. cursing the entire chimer race for the crimes of three people).
True, but sometimes I think that boredom and fear drove Azura as much as pride or vanity. Boredom because her only real constant source of amusemant as a Daedra Lord is meddling in the affairs of mortals or playing games with her Daedric siblings in which mortals are the pawns, and fear because the example of upstart mortals such as the Tribunal continuously resisting her machinations could inspire other mortals to do the same, thus depriving her of her fun and undermining her in the eyes of her followers.