Yes, I have experienced projection big time. This is what they do. You need to take the focus off her projection and concentrate on working on you.
You need to shield your children as much as you can from the MLC demon. This is to save their emotional health and well-being. Pulling them into your wife's tirades will only damage them. I agree wholeheartedly with Old Pilot. Work on making yourself the best husband possible as well as the best father.
Digging through your wifes trash is wrong. The ML'er looks at this as "control". You are now a guest in her house, you need to act like one. This all seems "trivial", but it matters to the ML'er. You have to start to see through the eyes of one.
Me: 46 H:44 Together: 25 years Married: 20 years Separated: 11-30-06 Divorced 12-21-07 OW: EA began 2005 PA began end of 2006 3 children,20, 16, 6 ex asked for forgiveness 01/16/11