Eure is the possessive pronoun for something belonging to ihr ("you plural" i.e. to several people whom you know well) for example: Eure hund ist klein = Your dog is small, (You being plural 3rd person informal), or "You people's dog is small"
Ihre is the possessive pronoun for something belonging to sie (fem 2nd person or plural 3rd person formal.) in the nominative case For example: Die Katzen trinken ihre Milch. The cats are drinking her/their milk, which one is correct will be entirely based on context.
I know it's a bit late and you probably figured it out already, besides the fact that I'm not a native speaker so i might be entirely wrong :P ... But perhaps this is helpful for someone else!
I understand 'Sie' can also be 'you' (sing. formal), and it's possessive yould be 'ihr(e)'