Then how do you reconcile this with Mesaana and Demandred wanting to rescue Semirhage from Rand, and Mesanaa telling Moridin it is their duty to rescue a fellow chosen? The reason they did that is because they wanted their Ally to survive.

With Graendal, she found herself completely alone. Moridin had Cyndane and Moghedien, Demandred was with Semirhage and Mesaana. Graendal was alone, as was Aran'gar.

It is completely logical for Graendal to give a leg up to Aran'gar. If she can resettle her somewhere, and give her power, that is another person for Graendal to manipulate. And since Graendal would have full knowledge of Aran'gar's base, and since Aran'gar is basically a moron, Graendal would have an extra power base with very little effort. Plus, Aran'gar had extensive knowledge of the Aes Sedai, which Graendal could exploit to throw a wrench in Mesaana's plan. With Semirhage captured and in bad odor with the DO, had Graendal destroyed Mesaana's plans, the Unholy Trio would have ended. Then Graendal could have more chances to move against Demandred, who she had already marked out as her chief rival after Moridin.

It also made sense to have support with you when the Dragon Reborn was in your territory and hunting for you.

Lastly, Graendal likes beautiful people with Power. Aran'gar surely qualified. She was a possible later addition to Graendal's collection.

As you can see, its all self-serving. There's obviously no kindness involved.