"Does your child like animals?"
Translation:Mag Ihr Kind Tiere?
You're right that there are several ways of translating "your" into German. However, "eure" is the wrong form here. Kind is nominative singular neuter. Therefore, your translation should read: "Mag euer Kind Tiere?". Other correct translations are: "Mag Ihr Kind Tiere?" and "Mag dein Kind Tiere?".