Hi,
you have to clearly distinguish between language copies and live copies, as these are 2 different concepts. Live copies are implemented by the MSM and you have the relationships between pages. Language copies are simple copies of the page, and there is not relationship between the "child" and the "parent" page; this relationships is just a very loose one based on the structure of the site trees and the name of the page; and of course it breaks if you start to modify the structure and/or the name of the pages.
With the MSM the situation is very different, because there each page knows the page it is inheriting from, and this information is preserved even if the child and/or parent page is renamed, moved, modified, etc. But of course that comes with a cost in terms of runtime performance and also administrative complexity and training for users. So it looks to me that you want to the use the MSM if you want to rename pages.
HTH,
Jörg
