Gordian Knot, You are one brave fella, and as Lenny says...a good man, but I think you are in for a hard ride. How, for instance, do you plan to deny access to the Internet, which seems to be the source of the infidelity? She sounds to be addicted to the Internet, first of all, and to this male acquaintance she has made. She is ignoring your home and children as a result. I sense that the **** will hit the fan when you set down this rule, and keep in mind, if she has mobility, there are other ways of accessing the internet, such as at a library or cafe.
I totally agree with Perna on this, that your caring exceeds the limits of most men (or women) in such a situation. Do you really think that counseling or psychiatric help is going to restore a happy household to the both of you? It sounds like she doesn't love you, and doesn't seem to care for the children either. Sorry if this sounds harsh, but you might be well-advised at this point to consult a lawyer with all this information, just to protect your custody rights.
Patty