Almost five years since I split with my second husband. The day after we split, we talked. I promised him that I would do my damnedest to keep things easy. In the early days that meant the girls being able to ring their dad whenever they wanted, and he would come and see them after school. I think they saw him more after the split than before. Gradually this settled into me having them during the week, and them staying at his at the weekends. They were 9 and 7 then, and now are 14 and 12.
We've never argued, though to be fair, we weren't a very argumentative couple, we just drifted apart. We're still good friends, and he'll come in for coffee when he drops the kids off. We're actually still married, I wanted to leave it two years for the no fault, and now I can't afford it.
We still co-parent and communicate about the kids a lot. He's still very much involved with my children from my first marriage, he raised them for ten years and has not walked away from them. He's a good bloke to be honest. So much so that we got back together a couple of years ago... it lasted only weeks.
My advice is communication, compromise and keeping your mouth shut. Don't sweat the small stuff. Their dad may do stuff differently to me, but his rules are his and mine are mine and the kids can whine about that all they want. We do back each other up, and any "well dad lets me do that!" is countered with: "those are his rules, not mine".
I think that personality can have a lot of bearing on a post-split relationship. People who always have to be right, or who consider their kids to be theirs are going to have more problems than adults who can concede that fault and blame on the parents part is best kept out of the arrangements. It's hard to let go of bitterness but worth it. My first marriage ended very bitterly. Lessons were learned. I'm back on speaking terms with him too, but it took 15 years.