Who babysits your children while she's out ****ing another man? Blunt... well yes but you need a good square kick in the ass to show you that you ENABLE her to be with another man if you're the one who is looking after your children while she galavants around. So... who looks after your children while she is in bed with someone else?
You cannot do ANYTHING to keep your marriage together if she doesn't want to be in it with you. Thing is you give her zero reason to want to be in it with her if you let her have him while living with you and benefiting from your income, your help with the bills, you're feeding her, having a roof over her head for when he tells her to go home, by babysitting and allowing her that freedom.
Go see your lawyer before she takes you to the cleaners both emotionally and financially.
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion