Turn undead doesn't turn you into an undead, despite how it sounds

Do you mean “turning” as in changing your direction on a battlemap? It seems like facing would be a factor during combat, such that, if you’re facing away from an opponent you’re likely at disadvantage to attack and/or they have advantage in attacking you (or whatever the bonus/penalty may be). I’m not sure how I’d handle the actual turning bit, if turning 180 degrees would constitute 1 full movement, and anything less than that can be done for free (or if all of it would be a free movement).

I generally like the idea, as anything that gives fighters more options and makes positioning important is great. I wonder though if Turning would need to be added as a reaction movement, since you could easily have a melee fighter just move to their opponent’s backside every turn to get an uncontested attack at advantage? So by making turning into a reaction, it gives the opponent a chance to respond, or gives at least gives them a decision on whether to use up their reaction for that or something else. I could see it making combat feel a bit more like a dance or a struggle to gain the upper-hand, which could be interesting for martial folks.

I use the optional facing rules from the DMG when I run games in a VTT that makes it easy to keep track of (TaleSpire for example, allows you to rotate minis)

Basically, the rules are that you have advantage when attacking the back hemisphere of a creature. A creature may use their reaction to face another direction when another creature moves. (I allow that rotation to continue throughout the attacking creature's turn to prevent players from moving a bit, to get enemies to face them, and then moving again after the enemy has used their reaction -- yes, there are players who will do that because they see the DM-player relationship as combative rather than as collaborative storytelling)

Shields only give the AC boost to the side that they are equipped on