because that is the feminine form of "ihr".
der Hund / die Katze / das Haustier
- Person: mein Hund / meine Katze / mein Haustier
- Person: dein Hund / deine Katze / dein Haustier
feminin: ihr Hund / ihre Katze / ihr Haustier maskulin: sein Hund / seine Katze / sein Haustier
- Person: unser Hund /unsere Katze / unser Haustier
- Person: euer Hund / eure Katze / euer Haustier
- Person: ihr Hund / ihre Katze / ihr Haustier
When it means "your" (belonging to the polite "you"), it's always capitalised, even in the middle of a sentence: Ihr.
"her" or "their" is lowercase, ihr -- except of course at the beginning of a sentence. There is absolutely no way to tell the difference between "her" or "their", except for context.
Is the "ihr" required here?
is it because the genders of Mutter and Vater differ
That's definitely one of the reasons it sounds wrong to me.
could it be "Ihre Mutter und Schwester"?
That sounds to me like "the person who is both her mother and her sister".
I wouldn't completely rule out the possibility of using it for "two people: (a) her mother, (b) her sister". But if you want to be clear, I would use the possessive determiner twice.