Preface: Like OneCatch, I have not personally experienced this difficult situation (though a close family of mine has gone through extended and repeated instances of this and has seen the light on the other side [ie recovered and still very much married]). Also, this is six days after your initial post so I acknowledge there's six days of life in which there may have been significantly changes to the field (hopefully there's been some progress made).
You say something which should give some hope: 1.) that he gets mad/ignores it when you bring it up, and B.) that it's very unlike him. Your dad may be feeling a significant amount of guilt and condemnation with no outlet for it (peer group, etc.). I imagine it would be a very difficult thing for a father to accept that he needs serious help from the people he's an established protector and covering over. It cuts right to the heart of a man, being shown evidence of being unable to do something, and especially if that something is providing for one's family. No matter how close your mom and dad have been in the past, this is something that would directly (and negatively) impact his wife's perception of him, so he may feel that he can't share it with him. But the fact that he gets so defensive means (to me) that this affects and troubles him deeply, and that he's desperately running from it because he can't bear to face what it's doing to his family. Furthermore, because of that he can't accept any course of action which would admit to himself or others that there needs to be some course correction.
It sounds like he loves you and your mom a lot, but doesn't know how to escape where he's at. He may be very fearful of what you both believe about him. He certainly needs (like *anybody*) a peer support group--men (and fathers) who he can confide in and share what's going on in his life. However, I think he first needs to know that home is a safe place for him to acknowledge that he's broken and also that his family is a crucial part of that support group.
If it were me in your dad's shoes (again, this is from my outside perspective, and the only information I have is that which you've provided in this thread), it would mean the world to me that my family saw through to my heart. Share with him that you believe in and *know* his heart for you and your mom, recalling specific times where he's shown that heart through his words and actions. You obviously have more insight into your dad than I do so I'll leave the particulars to you and your mom, but I think him knowing that he has the informed support of his home team would go a long way in getting him to take the next (and very needed) steps.
By "informed support", I mean that he needs to know both that you A.) Really know and believe in his heart for his family, and B.) Have acknowledged the hurt that has been caused to you and your mom but that it's in the midst of this that you support him and love him. Forgiveness comes from accepting the hurt and walking through it, not denying that it occurred.
We are definitely creatures of community. In all this, it is a good and needed thing for you and your mom to find a local (face-to-face) outlet to work through what's going on. Just like your dad can't do it on his own, you can't do this on your own. But even though you are in the same house, the needs of both you and of your mom are significantly different and need to be individually addressed.
Take care.