Yes, I do. No, it wasn't immediate and took some work. So, there's hope! I only read the original post, not all the responses, so hopefully this isn't too repetitive:
#1- Feel OK about things being bad between you, if you just broke up. Esp. if you have kids, would you really WANT to have broken up their family, if it's possible for the two of you to be perfectly nice, considerate and friendly to each other, right after the break-up? Wouldn't that make you wonder if you should still be together? The heartache of those first couple years of adjustment after you break up...as well as the periodic flare-ups later on, that remind you why you're a bad match for each other...are actually GOOD, because they remind you that the problem wasn't that you broke up, it was that you weren't right for each other in the first place. That doesn't make the conflict any less painful. But try to see it in its larger context.
#2- Put the kids first. If all the things you and your ex resent about each other are in the past (or are financial/property issues that will get worked out soon), that past will grow further and further away and be less and less important. If you constantly create NEW reasons for him to resent you, by bad-mouthing him to your kids, doing passive-aggressive things to make it difficult for him to exercise visitation or participate in things at their school, or by fighting with him in front of the kids every time he picks them up...those things will continue to fester, between you and your ex. Not to mention, all those things are rotten for your kids.
#3- Try not to give tit-for-tat. In each exchange, try to be the person and co-parent you know you ought to be - the type you wish HE'D be. In the immediate sense, you will have the satisfaction of knowing you're in the right. But more than likely, other people who influence him - his parents, your mutual friends, maybe even the kids themselves - will notice that you take the high road even when he's petty and may say something to him about it. You may never know about this, but it may - over time - influence him, nonetheless. Also, presumably this guy once loved you. AND you're the mother of the kids he (again, presumably) loves. So, unless you mated with a real monster, over time if he sees you taking good care of the children he loves and being reasonable, civil and cooperative with him, even in cases where he knows he's being a jerk to you... whatever burning anger he may feel toward you now will subside and he may even grow to appreciate you. Meanwhile, the less you allow yourself to get caught up in "keeping score" in battles with him...and the less guilty you feel, about behaving badly...the easier YOU'LL find it, to let go of YOUR anger.
#4- Get it out of your head that he will ever be other than the person you broke up with. If there was something seriously flawed about him and you broke up with him over it, it's a complete waste of time to keep feeling angry that he continues to have that flaw. Put your energy toward mitigating how that flaw affects you and your kids, if you can. Don't create useless conflict continuing to tell him what's wrong with him, or trying to convince him to change.
#5- The more comfortable, confident and happy each of you becomes in your lives apart from each other, the more you may realize that you were taking out your fears and insecurities about the future out on each other, by acting angry and hostile. As those insecurities fade, so may the hostility.
As to how a good relationship looks? My ex and I are both married now and very friendly with each other's spouses. His wife hosted my baby shower. My husband and my ex took my sons and step-son camping together. My ex and his wife come to our house every Christmas morning. Sometimes we celebrate part of Thanksgiving or other holidays together. We ALWAYS invite each other to any birthday celebrations for our kids. Sometimes we share a ride together, to the kids' events. All 4 of us (parents and step-parents) e-mail/text/call each other regularly, to share info. and plan things. We're flexible with our schedules. If we say no when the other wants to switch things around, it's only because we already had something planned, never because we're being a stickler for the schedule and refuse to cooperate. His parents still treat me like a valued member of their family and I arrange time for the kids to spend with them, as much as he does. My parents are also still warm toward him. Each of us tells the kids to respect the other. While we may joke with the kids about differences between the two households (there are a LOT), we both reiterate that it's OK for there to be differences. The kids know my reasons for doing things the way I do, but their Dad has his own reasons for doing things differently and he doesn't have to be exactly like me, for me to think he's a good Dad (and vice-versa).
...And things aren't perfect! I notice sometimes that his wife makes a point, in public, of clarifying that she's his wife and I'm the twins' mother; or she'll get irritated when people accidentally call me Mrs. Ex (assuming I have the same last name as my kids). It's awkward occasionally, but instead of getting offended, I try to see things from her perspective. There are a lot of people who are significant in her life now, with whom I have a significant history and she doesn't want to fall into being regarded as #2, she wants to be recognized as The Wife. OK. That's not so bad. And every once in a while, my ex and I will have a flare-up and I swear it hurts as much as it did when we were breaking up...and that makes me angry, because I don't expect to be that emotionally vulnerable to him anymore, yet suddenly there it is! But now I have my husband and my life is with him and he understands the dynamics and is always on my side (even if he may occasionally, gently point out where I've been unreasonable). So when I calm down, it's actually a relief to have had that bit of conflict to reinforce that I'm with the right person and everything turned out the way it should be. My ex and I may get along wonderfully, but underneath it all the fact remains that we were not meant to be partners. If we never broke up, we'd be making our kids miserable, fighting all the time and neither of us would have found our soul mates or been able to model for our kids what a good marriage looks like. Plus, my ex and I are BOTH motivated to return to the civility and friendliness we normally share, so we don't hold onto conflicts.
One last thought: It'd be nice to say that my ex and I bridging our conflict and becoming more civil was an equal, two-way street. But it really wasn't. I think ME letting go of my anger over things he handled poorly and just accepting and expecting him to handle things that way prompted HIM to improve, LATER. More specifically, he was irresponsible (not showing up for visits, paying C/S late), then he would compound the problem by consciously avoiding me, because he expected me to be angry and judgmental. When he stopped getting that reaction from me, he stopped avoiding me and started realizing, "It's NOT that she's a b****. I shouldn't miss my weekends and I should set up automatic payments, if I can't make myself remember my checkbook!" Problem solved...regardless that I "gave in" before he did.
Good luck, Mama!