If you want to follow the normal prescriptive rule, I think your stuck with either "my wife's and my," "my and my wife's," or a total rewrite, along the lines Glenda suggests.

Our instinctive sense that it's wrong, though, suggests that the prescriptive rule of case assignment (what I call "tricklle-down case") may not exactly capture the way English really works.

Descriptively, I think you would be most likely to hear "me and my wife's grief," apart from those who have so internalized the prescriptive pattern that they avoid "me and X" as a matter of course.

I believe what's happening here is that the genitive marker attaches not to the word but to the phrase/coordination (cf., "the duchess of York's dress"--it's the duchess who has the dress, not York; similarly, "Romeo and Juliet's love"). What we really have, therefore, is a coordination marked with the genitive:
 [[pronoun] & NP]'s, and the way English really works in such instances is to stick with the default, objective case for the pronoun. Note that you can also find people using the pattern [NP & me]'s, which lends support to my hypothesis about where the genitive marker tends to attach.

Karl

On Aug 17, 2013, at 7:14 PM, Geoffrey Layton wrote:

> I keep wanting to raise this question to the list, but somehow never have a good example at the time I think of it, but I just ran into an example that presents an excellent case of the problem of I guess what could be called a "double possessive" - where a noun and a pronoun are both used as possessives.
>  
> Here it is: "Words cannot describe my wife's and my grief" (from a news article). This construction has always struck me as exceedingly awkward, and my grammar instinct tells me it should have a solution based on another construction, but it escapes me.
>  
> Suggestions anybody? Or am I just being overly picky?
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