Respecting your ex-spouse may not be the easiest thing you've ever done, but it's necessary to make co-parenting easier on your children. Now that you have a separate household, your relationship with your ex should be about how to raise your children the best way you both can. The focus should be on them, not you. The strategies you develop now are about the welfare of your children, not your lousy marriage or playing the blame game over why it failed.
To that end, developing a courteous relationship with your ex is one of the most important ways you can make these years productive and nurturing ones for your brood. Look at it this way, other than yourself, your ex is the single most important person in your children's lives. The lessons they learn now about grace, cooperation, compromise and courtesy, they'll carry with them into their own adult relationships. For the most part, they'll be learning those lessons from the two of you.
If you have an issue to discuss with your ex-spouse, make sure to bring it up in private, not in front of your children. Avoid using your children as messengers or as confidants with which to discuss the failings of other caregivers. Cooperate when you can, and deal with conflicts diplomatically. If you're going to squabble about money or anything else, do it in private. The more united you appear in your joint efforts, the more successful they're likely to be.
If the going gets tough, remember that the problems you may encounter single parenting now won't last forever. When your children are older, your co-parenting arrangement will end, and you'll be free to move on to the next chapter in your life. Until then, grit your teeth, keep your own council and smile. Reward yourself every time you think of a disparaging, critical or negative remark in time, but don't say it. Your children are watching. Taking the high road will be hard sometimes, but when did you ever admire someone who didn't?