Draw out middle ground between the conflicting parents. Despite their differences, they both have school-aged children and likely have all the similar problems and joys that accompany that. According to Richard M. Highsmith of The Leader's Institute, this should be the first step so that both parties enter into the resolution process calm and amicable.
Allow each of the parents to state their grievance separately, without interruption from the other parent. Ask clarifying questions when necessary to bring any miscommunication to the surface.
Present several solutions to the conflict. It's helpful to include more than one alternative to avoid the appearances of bias and to give the parents several options from which to choose. Try to keep a win-win mindset so that no one parent will feel shorted in the suggested resolutions.
Request the conflicting parents to add their own suggestions. Encourage them to be creative and to work toward the common good in their solutions. Also remind them of any pertinent consequences that the school might inflict on the enactment of their suggestions.
Act upon the chosen solution or combination of solutions. Follow up by asking each parent how they feel about the situation. If necessary, inform the school of the issue, in case it continues.