Frau is feminine.
Hund is masculine.
deiner has the -er ending for feminine dative.
seinem has the -em ending for masculine or neuter dative.
For example, Wie geht es deinem Mann / deiner Frau / deinem Kind? Wie geht es seinem Vater / seiner Mutter / seinem Kind? "How is your husband / your wife / your child / his father / his mother / his child"?