Complicated Possessive?

Is "Daddy, me and the dog's favourite activity" correct?

Cos Because technically it's "Daddy, the dog and me's favourite activity", right?

'It is my favourite activity'. 'It is Daddy's favourite activity'. 'It is the dog's favourite activity' are all correct.

'Me's' is not. The possessive form of 'me' is 'mine'.

But you get into trouble if you try to combine these thoughts into a single sentence constructed the way you have. You could say 'It is Daddy's, my and the dog's favourite activity'.

That sounds really odd, though, if all you mean is 'Daddy, the dog and I all like ... most of all'.