“Nikki's and Alice's X” vs. “Nikki and Alice's X”
Consider describing the wedding of X and Y. If I want to avoid the overly-formal and poor-flowing "wedding of", it is more correct to say "X and Y's wedding" or "X's and Y's wedding"?
I acknowledge a very similar question has already been asked: What possessive forms are used for mutual 1st person ownership?
But unfortunately the example given is able to be easily phrased a different way and so respondents have been able to get away with avoiding the direct question.
Let's face it, we come across the need to get across the concept of mutual possession all the time and we don't always want to have to resort to the more tortured "Z of X and Y" as with the French language.
NB: In some cases, people get around this problem by dropping the apostrophes altogether and "adjectivising" the owners, especially if the owners are actually plural entities themselves. Eg. The "Mazda and Mitsubishi combined outputs" instead of the "Mazda's and Mitsubishi's combined outputs". Let's not let this muddy the waters though.