I'm really sorry to hear he's not fighting for the marriage. Mine manipulated our Relate sessions and we wasted a lot of time. I would so have appreciated the clarity that others have expressed that if he's not 100% committed to finding a way through then it's over, whatever you want, he just wants to make you the baddy by calling time. So he's a coward too. It really doesn't matter who brings an end to the sham this now is, no-one else will care or remember. I, eventually, realised that while my ex said yes to the 'do you want to make this work', the answer to the question 'you don't really want to be here do you?' was also yes. But, apparently, I ended the marriage!
Things had been increasingly rocky over the years since he did it but we'd had 3 children and it's so easy to miss what's really going on when you're also sleep deprived, busy and not wanting to. With hindsight he totally blamed me: 'if our marriage was good, I wouldn't have had the one night stand, I did therefore our marriage can't have been good (and that's obviously not my fault!)'. I could have forgiven at the time as I do think we're none of us perfect but the benefit of distance makes me question that now - it's not one decision to end up in bed with someone but lots and lots of points at which you could decide to do something different.
He's been a shit co-parent too and it's taken years of counselling to understand why I ended up being so unable to advocate for myself or recognise him for who he, now, is. But that has a lot to do with my upbringing (think stately homes thread) and my parents own divorce. It was painful, I resented and hated being a single parent for such a long time as I dealt with the pain of my children, which is, unfortunately, ongoing as they are desperate for the attention of a man who really only cares about himself.
But I'm now in a really good place, I have recognised myself and my strengths, I've helped my children navigate adolescence and early adulthood (just one to go) and have good relationships with them all now, though that was challenging at times. I did go on to have another long term relationship but ended that a year ago because it no longer met my needs. Covid has given me the time to recover and I'm very much looking forward to getting back out in the world and finding someone to share the next part of my life with. Or not, I'm pretty happy with my life.