Way I see it, receiving the stress from DD is part of the action.
Therefore, am I correct in thinking that if DD was your first action for the turn, while you could still trigger Push the Limit off of it, you would be unable to perform the second action due to having received stress (without being Tycho or having Captain Yorr nearby)?
I am fairly confident that Vader can't use his second action if DD was his first for the round, for that reason.
Unlike Expert Handling, it doesn't contain a "Free Action" prior to the receiving of the stress, so PtL and ExHand don't have triggers to nest..