The power of apppointment can be used either positively or negatively. Egwene can appoint sisters who oppose her to meaningless tasks or meaningless places without input from the Hall. An ally of Romanda could be sent to Arad Doman to distribute food, an ally of Lelaine could be given task of rat removal for Tar Valon, and if you really piss Egwene off you could be sent as a Windfinder instructor. On a positive note Egwene can make appointments that strengthen he position in the Tower. Silvliana is an example. Egwene got a very competetant Keeper and she made a gesture that would get Red support. Egwene can use appointments to weaken her foes and strengthen her supporters.

I think Egwene can rely on a few more than ten Aes Sedai. The Aes Sedai who really oppose Egwene are few in number. Most of the Aes Sedai will support Egwene because she is the Amyrlin. Romanda, Lelaine, and their handful of supporters will continue to oppose some if not most of Egwene policies, but I don't think they want to overthrow Egwene with Tarmon Gaidan just around the corner.

I guess we will have to disagree on the power of the moral suasion of Nyneave and Elayne. I think most Aes Seadai seeing Egwene being supported by the Queen of Malkier, defeater of Moggy, healer of the stilled, healer of the taint, healer of taint madness, healer of the weather, and the most powerful channeler in the Tower would give supporting Egwene a thought.