I'm surprised no one has answered.
We were married 20 yrs, estranged 3, divorced 9, and for the past 5 yrs are again living together because she needed help with the youngest (then 16, boy). We are still like oil and water (better than gasoline and flame) but now we share a quiet and mostly unspoken mutual respect.

Our marriage was an attachment of many expectations, largely frustrated, which are absent today (unless I'm overtired and cranky) We choose to be together because it benefits our children and grandchildren, and we both find contentment in that.

And we're not having sex, which may be the key to our co-operation, actually...

Conversation initiated by her about six months before leaving:
"I need sex every day and if I don't get it from you I'll get it from somebody else."[I did not recognize the fair warning]
"If you're gonna get it from somebody else you're gonna have to ask [I was wrong on that count] and if you're gonna ask anybody, ask me."
"I'm not gonna ask you and get rejected."
"I don't reject you. You reject me."

Beyond the obvious shortcomings of our communication technique, which always seemed to be based on a 'you vs. me' template, one could see within all those words the simple message, "I'm afraid."
"Does he still think I'm beautiful?"
"Do I really satisfy her?"
We didn't ask each other those questions. Well, she asked me but I did not realize the depth of her doubt so my simple "Yes." was not at all reassuring and I can tell you that I certainly did not ask her, I just made assumptions, probably about as accurate as 'she'd have to ask...'
Maybe the real reason we get along better now is that, having tried the alternative we discovered that, for us, it really IS better to find a way to 'stay together for the sake of the kids."

But what about YOU? Come on, now, I'm not the only one with a former spouse, am I?