First of all, I never really read any of the Ynnari rules, because I didn't want to lose our obsessions. And as far as I understood, including Ynnari units always meant losing obsessions. Or did I misunderstand?
But, I was reading through Phoenix Rising, and I read that when you decide to include Yvraine, the Visarch or the Yncarne, you can choose to remain Drukhari. (As long as there are no named characters or Coven units in that same detachment).
So, in short, can I have an Alliance of Agony (so including a Coven detachment), and put Yvraine in my Kabal detachment, and still keep my <Kabal> keyword? (Or in any Cult detachment that does not have Lelith)