They are actually living together! I really can't buy that any of the Forsaken would want to have one of their rivals around all the time. It's even implied that Aran'gar's presence is a bit annyoing for Graendal. And as it is seen, when the palace is actually attacked, they don't immediately form a link to defend themselves, but Graendal gets rid of Aran'gar.

Besides that, it still doesn't explain where Aran'gar & Delana (Delana's servant Miesa was probably killed off-screen) stayed for at least one week after her flight and before they moved into Graendal's lair.

I think the scene would definitely make somewhat more sense - as it was also suggested before ToM - if Aran'gar and Graendal by chance just had a meeting in the palace at the time when Rand arrived there (like we saw e.g. Sammael meeting Graendal in her palace). Of course, that probably wouldn't really work with having Delana there to perform Compulsion instead of the master of Compulsion, Graendal, or the other parts of the convulted twist to assure that Graendal outsmarts Rand..