You have made a difference in mine and Riley's lives ...
You have made a difference in my and Riley's lives ...
You have made a difference in Riley's and my lives
Not sure what to use here.
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The first is incorrect. Either of the other two will work, but I’d prefer the third, if only because there is (or at least used to be) a cultural convention for putting oneself last in a list. So, “Pugh, Pugh, Barney McGrew, Cuthbert, Dibble, and I all went for a pint after putting out the fire”.
A way to see this is to try each form with only the my/mine in it. So the first one becomes (with plurality adjusted as needed):
You have made a difference in mine life.
That is clearly incorrect.
Note, however, that the above method doesn’t always work. For example, suppose we were talking not about me and Riley, but about John and Riley. Then the method above would suggest that the correct wording would be:
You have made a difference in John’s and Riley’s lives.
And that the following is incorrect:
You have made a difference in John and Riley’s lives.
(Because if you test it as before by removing “and Riley’s”, it breaks)
However, in this case, the second style is allowable, and in fact is probably more common. There is a technical name for this — i.e. for restricting the use of that possessive ‘s to only the last item on the list - but I can’t remember what it is.
ADDED: the phrase I was looking for is compound possession.
Don't worry; we English speakers aren't sure either. The options given are more or less all in free variation.
Particular regions, style guides, or high school English teachers (of which I am one) may recommend one or the other, but listen to regular conversation by native speakers and you'll likely hear all of them at some point.
That said, I would say the first option is the least common. (Same with any use of a possessive pronoun in that slot: hers, ours, yours, theirs).