You really should try to answer your questions before asking them.
The simple way is to sort the two letters before concatenating them and using the result as the index:
Add
sub get_index { $_[0] lt $_[1] ? ($_[0].$_[1]) : ($_[1].$_[0]) }
and replace
$counts{$site1_parts[$i].$site2_parts[$i]}++ while ($i--);
with
$counts{get_index($site1_parts[$i], $site2_parts[$i])}++ while ($i--);
my @site1 = qw( AGTTTT );
my @site2 = qw( GAKKHT );
gives
AG: 2, HT: 1, KT: 2, TT: 1
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