"She is not playing with her man."
Translation:Sie spielt nicht mit ihrem Mann.
not sure but maybe because "Mann" is masculine. "Der Mann" in dative would be "Dem Mann", so that ending in "-m" might be present in this case. Perhaps.
From what I can gather the word "mit" makes this dative so you have to use ihrem for masculine and neuter nouns and ihrer for a feminine noun.
It is in the dative case. German has a dative case which includes 'with' (unlike other languages that replace that with instrumental). Ihr/her becomes ihrem Mann because Mann is the indirect object and also masculine. To give a few examples of dative: Ich spiele mit meinem Mann. Masculine dative. Ich spiele mit meiner Frau. Feminine dative. Ich spiele mit meinem Kind. Neuter dative. Ich spiele mit meinen Eltern. Plural dative.
If you forget how the declension works then you can refer to Wikipedia which has a nice article regarding German grammar and lists the words and their endings at the bottom of the page. It also includes endings for the Nominative, Accusative and Genitive cases.