Upon the presentations of the Court of an appropriate Motion for Rule for Contempt, in any domestic relations proceeding, upon same having been appropriately and properly verified by the moving party, the Court may, upon being requested to do so, and in instances where the nature of the proceeding relates to the payment or non-payment of child support and maintenance; visitation, or the denial of same; or such other matters, as the Court deems appropriate, the Court may issue the Rule prior to the next regularly scheduled announcement of the Motion Docket, in order to expedite the Service of Process of same, and in order to eliminate unnecessary delays in proceeding in such matters, when same demand the Court's immediate attention.