It is the public policy of this state that parents shall be responsible for the support of their dependent children in order to relieve or avoid the burden often borne by the general citizenry through public assistance programs. The existing remedies pertaining to family desertion and nonsupport of dependent children may be augmented by the additional remedies as provided in this chapter, which are directed to the resources of the parents. These remedies are intended to be additional to those provided under existing law.