Confirm that the character, their weapon, and any other cards played as a result (such as from a play or band ability) must all complete BEFORE any other triggers (like on Angel's Sword) can activate.
The phrase “play the first enhancement” indicates a play an enhancement ability that takes effect as a response to the initial blocker(s) being presented.
In order for it to 'respond', it must wait for all abilities to complete. Angel's Sword (and any other 'play first' abilities) cannot insert themselves between abilities.
In the example given, the EC blocks, D2, plays, then does whatever else happens as a result. Once abilities stop, THEN an enhancement could be played. This is a consistent ruling, and has been the case as long as I have been reading ruling threads and interpreting rules.