Do I have any objection to the construction “a friend of mine” or “a friend of yours”? Well, no. I would never say “a friend of me” or “a friend of you”. And yes, you would say “a cousin of my mother’s”, “a child of hers”. Well, “a friend of the footballer’s” is the same thing! The only time you drop the double possessive is when, instead of being involved with an animate being, you are “a lover of the British Museum”, because obviously the British Museum does not – and never can – love you back.