She has recently moved out into her own place. I guess what I'm asking is what do I say to her? Or should I even say anything to her? Tell her I know about the A and that it's unacceptable then gather the rest of her stuff up and put it outside?...
Ah! No worries about throwing her stuff out. The reason she moved out was so she could continue her affair unabated the constraints of husband and family.
You need to see a "family" lawyer to find out about the laws in your state regarding child custody, separation and divorce. If your finances aren't separated, then go ahead and separate them. Be sure to setup a visitation schedule for the children.
Move on with your life assuming she's not going to be a part of it.