Atani would take both packets of damage, due to its ability. It would take both packets of damage simultaneously, but they would resolve at the same time.

Since the card hasn't entered play yet, it is not a card you control. Thus, it can be interrupted and removed from the game. 401.1 A player controls his hero, each card he puts into play, and each link he adds to the chain. Cards in other zones have no controller. Actually, it IS a card you control...