Which are correct:
1) Some children of my friends like to ski.
2) Some children of wealthy families like to ski.
3) Some of the children of my friends like to ski.
Could '3' be used to mean: 'Some of the children of some of my friends like to ski.'
I think '3' could be interpreted that way.
'2' sounds fine to me, but for some reason '1' does not.
They all mean the same to me. Some children that the hearer doesn't know or care about like to ski. They are not likely to ask whether you mean some of the children of all of your friends, or all of the children of some of your friends, or only some of the children of some of your friends.
You could say "Some of my friend's/s' children like to ski." They'll let you know if they're interested in where the apostrophe should go.