When New York couples separate or divorce, they often face a number of hurdles in their quests to successfully move on to the next stages of their lives. One of those hurdles is putting together a child custody arrangement that respects the children's need to have a warm and constructive relationship with both of their parents. That may take quite a bit of sorting out. However, the story doesn't end when the child custody arrangement is established and approved by a judge. It just begins there, with the next chapter being about co-parenting successfully, especially if one or both members of the original couple remarry.
When a remarriage happens, there can be serious jealously issues. A father may feel that he is being replaced by his former partner's new husband, or a mother may feel that she is being replaced by her former partner's new wife. Those feelings are real, and need to be talked about by those involved, so they don't wind up having an adverse effect on the children.
Also, co-parenting with your former partner and their new husband or wife is much more than keeping to a set schedule. It also involves clear communication about basic facts of the children's lives. Those facts can include a child injuring a knee, making a new friend or being nervous about a new activity. Clear communication about such key facts is critical for successful co-parenting.
Of course, co-parenting also requires everyone in parental roles being on the same page about some things. Those things can include diets and bedtimes. They can also include the values that are to be imparted to the children. When everybody who is in a parental role agrees about basic values to teach the children, they are assuring that the children will get consistent standards.