I hate to say it but your mother is right LOL! In every book I own on bird care (and believe me I have a most extensive library) the ones that talk about cage placement tell you not to place near a window, this is to both guard against the heat of the sun which can cause death and also to keep from drafts which cause respiratory illness in many birds.

We do have some of our cages situated near windows. We make sure the windows are not facing the rising sun and also do not open the windows for drafts. Now on the other had when it is plenty warm the windows can be open (but not only does the temperature need to be warm but the wind if there is any needs to be warm as well).

Do not keep near a window in cooler weather or in extreme heat. It is a health risk.