When both parents live with their children and are mutually committed to them, is likely to form?

"A parental alliance" is likely to form.

A parental alliance is an agreement between parents that they will cooperate with the goal that the sum of their child rearing and care will be more noteworthy than the two, isolated, parts. The alliance works with the goal that each parent improves the other parent's qualities, and helps smooth off any unpleasant edges.

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