Question regarding Malachai end fight

Here's my question.

I killed Doedre Darktongue, and turned Malachai's lungs over to Piety. Had to go to work.

Came back later, and killed both Maligaro and Shavronne, and turned those organs into Piety. I then get the quest to enter the Black Core and Kill Malachai.

When I try to enter the black core, it tells me I have to kill his 3 guardians.

Do I have to kill all three in one sitting, and only THEN can I enter the Black Core?

that would kinda suck, because if I kill 2, and then my wife calls me away for 15 minutes, I have to start all over again....

Yep.

If you go afk IN the instance, it wont close on you. If you exit the instance/close the game, and it's more than 8-15 minutes, then the instance will close by itself.

Yes that's how it works. To access the core you need to kill all 3 every time you reload the zone. It only takes a few minutes to clear the whole thing and you only do it 3 times (once per difficulty) so not a big issue.