If they respond to kaalia's trigger, then you haven't even chose which card to put onto the battlefield.
If they try to destroy it after you've declared you're putting in Avacyn, then it's too late, because she's already in play.
Do note that if you jump the gun and dump in Avacyn without waiting for responses, then they can tell you to back it up because they want to respond to the trigger.
You'll still get the chance to put in Avacyn no matter what happens to kaalia.
This situation recently came up in our playgroup.
I declare my Kaalia of the Vast as an attacker, attempting to bring out Avacyn, Angel of Hope. He taps his Royal Assassin to destroy my now-tapped Kaalia of the Vast.
Does Avacyn, Angel of Hope save Kaalia of the Vast from the Royal Assassin's ability, or does the Royal Assassin's ability destroy Kaalia of the Vast before Avacyn, Angel of Hope can save her? If the latter, Avacyn, Angel of Hope will nevertheless appear on the battlefield, will she not?
Thanks in advance for your time.
The Great Creature Token Project
If they respond to kaalia's trigger, then you haven't even chose which card to put onto the battlefield.
If they try to destroy it after you've declared you're putting in Avacyn, then it's too late, because she's already in play.
Do note that if you jump the gun and dump in Avacyn without waiting for responses, then they can tell you to back it up because they want to respond to the trigger.
You'll still get the chance to put in Avacyn no matter what happens to kaalia.