I'm not being deliberately obstinate (or, worse still, obtuse) but when I come across a word or sentence (as I did a few days ago while reading a British newspaper,) that sounds unnatural or incorrect, I like to get to the bottom and ask a native speaker.That's what UsingEnglish.com is all about, isn't it? .
It's certainly one of the things we are here for.
However, not everything in language can be tied down precisely - even by native speakers who have studied their own language for many years. Some combinations of words, while apparently grammatical, appear to seem somehow wrong to most native speakers. Showing that they have been used on occasion does not prove that they are generally accepted or used.
My personal opinion is that the 'weak' possessives,
my your , her, its, our and
their, cannot normally be coordinated, while the 'strong possessives,
mine, yours, his, hers, ours and
theirs, can:
*/? I showed them my and your picture.
I showed them mine and yours. :tick:
(I omitted his from the list of weak possessives, because it is identical to the strong form; and its from the list of strong possessives, because it is rarely used).
On those occasions when people who have not prepared formally what they are going to say are in a position where they are about to produce coordinated weak possessive, they generally make the first one strong. Thus 'my and your picture ' is generally rendered as 'mine and your picture', and even as 'mine and yours picture
'.
Having said that, some combinations appear to be less unacceptable than others. This is my idea of the acceptability:
my, its and ... - generally unacceptable
your, her, our, their and ... - less unacceptable
his and ... - acceptable, because it could be the strong form
I stress that this is a personal opinion. We may get something more solid from others.
ps. I am working my way through this to see if it helps:
http://www.ciscl.unisi.it/doc/doc_pub/MatteiniPHD_Thesis.pdf