When you and your ex start co-parenting, don't think of it as something that the two of you have to do together -- that you're obligated to do. Instead, think of it as something that you can do for your kids. You want to put them first. You know that staying involved with both parents is best for them, so the two of you can set your differences aside and put the kids first.
This mindset alone can help you get around a lot of disputes and arguments with your ex. Every time you feel angry or frustrated, it helps to remember that it all centers on the kids. Yes, it's not perfect for you. No, you may not always enjoy coordinating with your ex. But if that gives the children the best possible future, isn't it worth a little bit of a sacrifice on your end?
One way to do this is to make requests, not demands, when talking to your ex.
Instead of telling your ex he or she has to put the kids to bed earlier, for instance, try asking "Would you consider putting them to bed at 8:00 so that they can have the same schedule at both houses?" Instead of demanding that your ex picks the kids up from school or takes them to activities, try saying "This is the only way they can really stay involved. Would you please do it so that they don't miss out?"
By asking questions, you make the whole thing less contentious, and you focus the arrangement back on the children.
As you move forward with this new phase in your life, make sure you know what custody rights you have and what legal steps you can take if your ex ever violates those rights.