Despite being a native speaker of American English, I cannot find a construction that sounds natural when trying to form a possessive from coordinated subjects including a first person pronoun, like "He and I" or "My brother and I." If it's "You and I," I can just use "our." But what is the proper way to form a possessive in these other instances?
The cat which belongs to my brother and me ran away.
- ? My brother and I's cat ran away.
- * My brother's and my cat ran away.
- */? Me and my brother's cat ran away.
Oddly enough, the one which sounds the most natural to me (and which I hear most often in natural speech, is the last: "me and my brother's." My hypothesis is that this is used to avoid the issue with the first-person possessive form, but that could very well be wrong.
However, I'm not sure this is the best answer, either, as it introduces some pretty bad ambiguity in some places.
A person who is a friend to both my brother and me got married yesterday.
- */? Me and my brother's friend got married yesterday.
I think you can see the obvious problem.
What is the proper way to possessivize coordinated first-/third-person subjects?
Edit: I would much prefer an answer which does not require rephrasing the entire sentence.