Hi,
You could use a positive lookahead like this:

 use strict;
 use warnings;
 
 my $regex = "\\default\\main\\TSDEMO\\WORKAREA\\tsdemo_intranet\\TSDE
+MO\\images\\corner";
 my $website = "TSDEMO";
 $regex =~ m/($website.*)(?=\\$website)/gi;
 my $parent = $';
 print "$parent\n";
[download]

But what is wrong with concatenating the $website variable to the result?
BTW your (and my) code does not find the second but the last occurance of $website.
si_lence