If you're parents, it's always in your children's best interest to co-parent in a friendly and mutually respectful manner. Divorce is always painful. When one parent demeans the other in front of their children it can create life-long emotional wounds. If need be, seek out a therapist or coach to help you devise a co-parenting plan and develop effective communication skills. Ask yourself, "What's more important--my anger and resentment or the health and well-being of my children?"
In situations without children, if one person still has romantic feelings or the desire to get back together and their ex doesn't feel the same, friendship usually doesn't work. The one longing to be a couple continuously feels rejected, which invokes feelings of guilt, frustration, and/or resentment in the other.
Examine your motives for wanting to stay friends. Hidden agendas such as financial or material gain, fear of being alone, appearing desirable to others, or relieving guilt will ultimately contaminate the friendship. When someone uses another person for their own gain, sooner or later the person being used becomes resentful and the relationship implodes. There has to be a mutual benefit. These can include enjoying a supportive friendship with someone you care about and who cares about you, maintaining a shared social circle, or for ex's who work together, being able to have a positive relationship at work.
In or out of relationship, it's important to develop your own self-sufficiency and independence, including having your own friends and support system. Your ex can be part of your support system, but being emotionally dependent on someone else is always a recipe for disaster.
Boundaries also need to be communicated. Discuss how much contact you both want with and from each other. If there's a disparity, work to find middle ground that will work for both of you. Talk about how you want to handle new people in your life. Some people are comfortable knowing all about their ex's latest date, while others may not be ready to hear it.
Introducing a new person into the equation can work if the two ex's have maintained a healthy friendship over an extended period of time following their break-up. If you broke up with your ex a month ago, it's probably not going to work to bring him into your new relationship because you haven't had time to solidify the platonic friendship.
If you've shared an active friendship with your ex for a year or more since the break-up, give the new person in your life the opportunity to meet your ex, so she can be reassured that you're truly just friends. If you've included your new lover in your friendship with your ex and they don't click, respect their feelings and participate in the friendship with your ex on your own. If your lover demands that you cut your ex out of your life, pay attention to this red flag. You may be dealing with someone who is insecure or emotionally immature.
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