The court shall, as set forth in this chapter, have exclusive original jurisdiction to determine all cases of adults involved in matters arising out of § 14-1-5(3) and all cases of adults charged with:
(1) Being responsible for or contributing to the delinquency, waywardness, or neglect of any child under sixteen (16) years of age;
(2) Desertion, abandonment, or failure to provide subsistence for any child dependent upon him or her for support; or
(3) Neglect to send any child to school as required by law.