I am in a similar place and my heart goes out to you.
I installed a keylogger on my SAWH's laptop and phone mid September, which confirmed what, deep down, I already knew - he has a massive addiction. Current situation is that he will not discuss it at all face to face and I have emailed him daily for the last 24 days (not aggressively, just trying to get some communication going) and he has not opened a single one. He simply feels that if he doesn't acknowledge it, then it hasn't happened.
Screenshots say otherwise, my conversations with many OW say otherwise, and last, but not least, my own conversations with him with me pretending to be OW on four different occasions over the last year, say otherwise.
I am within days of being ready to say "start facing up and talking, or I leave". It's been really, really hard to come to this. I love him so much and the last thing I want to do is go.
It's shockingly painful - for me it's been two and a half years and each discovery feels like the first and, finally, enough is enough.
Be strong, do what is right for YOU and your kids, not him - he's got to shape up or ship out and gave up the right to expect you to stay the first time he cheated on you - addicted or not.
Look after yourself - it's what I'm doing now, finally.
Me 43 (BS)
Him 51 (SAWH)
DDay (too many to mention), but 1st 06/2011
Children - two, mine from my previous marriage
You're braver than you believe, and stronger than you seem, and smarter than you think (A A Milne)