> For anyone out there attempting to back up their data 
from 
> a MyFamily-hosted website, I've concluded after hours of 
> testing that, although WinHTTrack is a fine product, it 
is 
> not capable of performing this task.  

You did try the "Capture URL" feature, starting from the 
login page, did you? 

> My thanks to the developers for their advice.  My search 
> for a solution continues elsewhere.

Form-based sites which mix cookies and redirects are 
generally hard to handle, and sometimes impossible.