Whenever application is made to the conciliation court for conciliation proceedings in respect to a controversy between spouses or a contested action for annulment of marriage, dissolution of marriage, or legal separation, but there is no minor child whose welfare might be affected by the results of the controversy, and it appears to the court that reconciliation of the spouses or amicable adjustment of the controversy can probably be achieved, and that the work of the court in cases involving children will not be seriously impeded by acceptance of the case, the court may accept and dispose of the case in the same manner as similar cases involving the welfare of children are disposed of. In the event of such application and acceptance, the court shall have the same jurisdiction over the controversy and the parties thereto or having any relation thereto that it has under this article in similar cases involving the welfare of children.