Except that for an actual Priestess of Bhaal, her first order of business would be to help secure Bhaal's return--by killing CHARNAME. Go ahead and explain it away with her "mental instability" if you want, but the fact remains that if she serves a Bhaalspawn, she is violating Bhaal's direct orders, ergo she is NOT a Priestess of Bhaal. What you might do is explore the generation gap issue: Her parent(s) worshipped Bhaal, but now they're dead and so is he, and she chooses to worship one of his kids instead, because he's hip to the modern lingo, not like that old Bhaal fuddy-duddy who was the ultimate deadbeat dad. Of course, as soon as she formally declares that she's no longer going to obey Bhaal's plan for her, her non-removable Bhaal artifact should immediately reject her, and she can't use it anymore. Whether or not CHARNAME (or Imoen/Sarevok) would be able to use it, that's a bit more likely.
As for her being a Cleric: Priests of dead deities flat-out have NO casting abilities, unless (as you stated) their spells are granted through some artifact, or they find a substitute god to pray to. Your Priestess of Bhaal would have to fudge some devotion to someone like Cyric or Kelemvor, or become a very sorry excuse for a Fighter. That's why you might get more mileage out of making her a paladin or ranger who worships Bhaal (or one of his backstairs upstarts), instead of a Cleric, as a Paladin with no spells could actually still hold her own until CHARNAME gains enough control over the essence to start granting spells to her. Not to mention that non-Good rangers/paladins is a kickass idea, with hitherto virtually unexplored roleplaying potential.