It seems to me that the count of individual di-peptides in each sequence does not matter, but only the number of unique (overlapping) di-peptides found. If I understand this correctly, here's another approach, including some approaches from other replies (with some debug statements):

c:\@Work\Perl\monks>perl -wMstrict -le
"use Data::Dump;
 ;;
 use constant DIPEPS   => qw(AA AL DA DE DV VD DW QD SD HD ED DY VE EN
+ EI KE NV VP FV SS WK KK);
 use constant N_DIPEPS => scalar DIPEPS;
 ;;
 my ($dipep) =
   map  qr{ (?i) (?: $_) }xms,
   join '|',
   DIPEPS
   ;
 print $dipep;
 ;;
 my %count;
 for my $seq (qw(AAALVDENEC AATLVDEGDG)) {
   $count{$seq}{$1} = 1 while $seq =~ m{ (?= ($dipep)) }xmsg;
   }
 dd \%count;
 ;;
 for my $seq (keys %count) {
   my $sum = keys %{ $count{$seq} };
   my $abs = N_DIPEPS - $sum;
   print qq{$seq: sum = $sum, abs = $abs};
   }
"
(?^msx: (?i) (?: AA|AL|DA|DE|DV|VD|DW|QD|SD|HD|ED|DY|VE|EN|EI|KE|NV|VP
+|FV|SS|WK|KK) )
{
  AAALVDENEC => { AA => 1, AL => 1, DE => 1, EN => 1, VD => 1 },
  AATLVDEGDG => { AA => 1, DE => 1, VD => 1 },
}

AAALVDENEC: sum = 5, abs = 17
AATLVDEGDG: sum = 3, abs = 19
[download]

Update: And another approach, based on the same (mis?)understanding that only the number of unique di-peptides matter and not their individual counts:

c:\@Work\Perl\monks>perl -wMstrict -le
"use List::MoreUtils qw(uniq);
 use Data::Dump;
 ;;
 use constant DIPEPS   => qw(AA AL DA DE DV VD DW QD SD HD ED DY VE EN
+ EI KE NV VP FV SS WK KK);
 use constant N_DIPEPS => scalar DIPEPS;
 ;;
 my ($dipep) =
   map  qr{ (?i) (?: $_) }xms,
   join '|',
   DIPEPS
   ;
 ;;
 my %count;
 for my $seq (qw(AAALVDENEC AATLVDEGDG)) {
   $count{$seq} = uniq $seq =~ m{ (?= ($dipep)) }xmsg;
   }
 dd \%count;
 ;;
 for my $seq (keys %count) {
   my $sum = $count{$seq};
   my $abs = N_DIPEPS - $sum;
   print qq{$seq: sum = $sum, abs = $abs};
   }
"
{ AAALVDENEC => 5, AATLVDEGDG => 3 }

AAALVDENEC: sum = 5, abs = 17
AATLVDEGDG: sum = 3, abs = 19
[download]