My question revolves around the following scenario:

I team attack Poison Ivy with Hawk and Dove. No additional effects are played.

I ask my opponent to select to whom Poison Ivy will be dealing her damage. He selects Hawk. I then play From The Shadows, giving Hawk +5 DEF, and saving him from being stunned.

My question is, was this a valid play? Do I have priority to play effects after the defender of a team attack selects its target?

I apologize in advance if this question has previously been addressed, and if it has, I would appreciate it if someone could direct me to the appropriate thread.

You can't do that. You totally finish calculating ATK and DEF. All effects are over. Attacker obviously applies his ATK to your DEF. You then choose who to apply your ATK to and there's nothing that can be done by the attacker except take the damage.