Others, can pull it off, but it's EXTREMELY difficult on them.
It is a rare, rare few -- maybe 25% of the 10% who can even do this -- that can do so dispassionately, like they can get into "game mode" without it affecting them emotionally (or even physically).
There is no shame in admitting you're part of the middle group. I was. I needed anti-anxiety/anti-depressants just to get thru it (which are NOT a bad idea, btw). But you do have to minimize all of the superfluous "drama" which is why I've been trying to get you to keep this NARROWED to the task at hand.
Keeping your daughter from returning home was a TEST, on Day 1 post-confront, and you failed it. Not a huge deal -- you can get back up on the horse today -- but you do need to let her know that you'll BOTH need to stick to what's been agreed when it comes to your daughter. "She's tired; she fell asleep" is not a sufficient excuse.
If you don't think you can "come across as the calmest, most reasonable guy in the room" when talking to her mom and aunt, then put off talking to them until you can. Nothing wrong with that. TRUTH is something that can be told at ANY time.
Bottom line: you need to focus on right now, in order:
1. Your daughter.
2. Your own moves.
3. Your interactions with your wife. (Learn to draw and enforce boundaries, without angry outbursts, and co-parent civilly).
Who's seen-whose-truck-where is way down the list.
