Here's my perspective on your interchange with W -- it was very helpful that you posted it all. W was upset that you "stuck her at home to deal with S6". That's really what it was about, she felt that you left her alone to deal with him while you went off and had fun. Everything else was a red herring.
When you then got into the discussion of what you told S6 and when, it didn't matter. There was a 0.0% chance she was going to absorb what you were saying, stop and think, and say "Oh! I see he's right, I should apologize." In fact, the more you rebut her version of events, the angrier she's going to get, and will dig in more and more, or will move the ball to be angry about something else.
It is never productive to discuss facts with someone who is emotional -- ever. There is no judge or jury, and you cannot win.
What you need to do is comment on and validate the other person's emotions:
"W, I can see that you're upset by how things have happened this weekend. I'm sorry you feel that way, I'm sure it's frustrating. My conversations with S were different than what he's telling you, but that's not what's important right now."
Try to empathize with how she's feeling and validate it. When she calms down she may ask for your version of events, or she may not, but either way it doesn't matter. Even if you were 100% right she's still mad at you right?
If you feel that you were treated unfairly, the best way to handle it is to say "W, I didn't like how the discussion about the lake went. I'd like to talk to you about it some more (pick a time later)"
That way she has a chance to mentally prepare and will be more likely to be receptive. Then open up that discussion by explaining how you think she felt about it, or how it seemed from her perspective, explain your perspective, and fully own anything you believe you did wrong without asking her to do the same.
Good luck!
Acc
Married 18, Together 20, Now Divorced M: 48, W: 50, D: 18, S: 16, D: 12 Bomb Dropped (EA, D): 7/13/11 Start Reconcile: 8/15/11 Bomb Dropped (EA, D): 5/1/2014 (Divorced) In a New Relationship: 3/2015