Simon,

I think being weak does have something to do with it if the clubs that she is using are heavy. Most ladies club are light enough for them. Does your wife has ladies club?
My wife's swing used to be quite upright when she used to just pick up the clb with her arms on the back swing and not her shoulders and it became flat when she tried to swing more with her shoulders.

The thing that most people misunderstand(i think) is that the golf swing is only a shoulder turn. This is true to a certain extent but once your swing gets to the half way point, you also have to use your arms as well (not stopping the shoulder turn ofcourse!).

Thats just my opinion though.