I was having a bit of trouble following some of the information you provided.

By default HTTrack will not follow onto domains external from your starting
domain.  So if you start on www.xxxx.xx and there are links to www.yyyy.yy
then those shouldn't be followed.  So do you have filters (scan rules) to
follow to external domains/sites?
Is www.yyyy.yy password protected?  Using the same authentication method as
www.xxxx.xx ?  If so then you would probably have to add a... hmm... I was
going to say add a filter with user:password@ details but I'm not sure that
works in a filter.