She's not cheating on you because you are making her watch the kids Wednesday night.
(Probably mis-)Quoted from David Deida's "The Way of the Superior Man": Her complaint is content free.
Her spaz about Wednesday night is a reflection of her emotions regarding your relationship. You have to learn to read between to lines to see what she's REALLY saying when she complains.
Trying to logic it out with her is going to make it much much worse.
Would have been a great opportunity to validate her feelings:
"I didn't realize you had plans that evening. You seem to be very angry and upset about this, and I can see why. If I were in your shoes, I'd be disappointed too"
Me: 35 Her (WAW): 34 D8, S5, D2 T:16, M:9 BD + D: 4/3/2015 EA Confirmed 5/6/2015 Separation under the same roof