All proceedings involving a family relations matter shall be first placed on the family relations docket of the Superior Court; and except for juvenile matters which are provided for in § 46b-133, the judge before whom such proceeding is brought, may transfer such matter to the criminal or civil docket of said court if he deems that such docket is more suitable for the disposition of the case. Any case so entered or transferred to either docket shall be proceeded upon as are other cases of a like nature standing on such docket.