John's and George's mother went shopping.

[99bottles]

I read somewhere that I should put apostrophe only after the second name, unless they have different mothers.

'John and George's mother went shopping.'

But why? Doesn't the fact that the mother is only one make it clear that both of them have the same mother? Something else that troubles me is that putting only one apostrophe makes it ambiguous, since it sounds like two people went shopping: George's mother and John.

 

[cereal_chick]

Think of it like this: "John and George" is a single noun phrase, therefore it's entitled to only one possessive marker. "John's and George's mother" just sounds weird to me; I'm not sure whether it's outright wrong, but it's not something I'd ever say.

As for your second point, we use intonation to distinguish between the two cases in speech. If they both have the same mother going to the shops, we put equal stress on "John" and "mother" and we don't stress "George" as much, whereas if John is accompanying George's mother to the shops, we put equal stress on all three of "John", "George", and "mother". In writing, if you really wanted to be unambiguous, you'd just rewrite it.

 

[Tdol]

John went shopping with George's mother would be a natural way of saying that two people went.

 

[Phaedrus]

John went shopping with George's mother would be a natural way of saying that two people went.

Or, if each went shopping independently of the other (perhaps they were on the same outing but went to different stores), we could simply put the lady first:

George's mother and John went shopping.

 

[Tdol]

Also, we could use with to make things 110% clear.