Whatever her complaints about you there is no excuse for her to cheat. I think she has lost respect for you partially because of the employment situation, that is the first thing to be rectified.
Secondly, you need to GAL. I joined one of those meetup.com groups. It was almost comical how quickly my W wanted to suddenly start going with me to them. I mean heaven forbid there might be females who I might start chatting to. Bear in mind until then she constantly refused to go on dates with me.
Let your W watch the kids for a change, dress up, go out, meet new people
I'm not saying to go out and get laid, but socially interact with new people, get your cell phone blowing up with texts from your new found friends, watch and observe how curious she suddenly becomes.
The reality of the situation is that any long term OM is going to run 15 miles once faced with the reality of a married woman with 5 kids. This is why she needs to move out but you must not do anything to financially enable her. This is her choice so she needs to finance it
50/50 childcare arrangement is what you want, good luck to her finding an apartment big enough for 5 kids! Maybe one week of, one week on? This is the only way for her to sniff the new reality. She may or may not come running back to you? Either way you will be fine !!
