Using the print method of Text::CSV_XS, eliminating $hash2 totally, and eliminating the {info1} level instead just assigning an array ref to $hash1->{$ID}.

#!/usr/bin/perl
use warnings;
use strict;
use diagnostics;

my $hash1;

use Text::CSV_XS;

my $sep="\t"; 
my $csv = Text::CSV_XS->new ({ sep_char => $sep });

open (my $file1, "<","wholepedigree_F.txt") or die "Couldn't open whol
+epedigree_F.txt \n";
while (my $row = $csv->getline ($file1)) {
     next if ($.==1);
     my ($ID, $sire, $dam, $F, $FB, $AHC, $FA) = @$row; 
     if ($ID){
        $hash1 -> {$ID}= [$F,$AHC]; 
        }
     }
close $file1;

my $Output=\*STDOUT; 

open (my $file2, "<","damF.txt") or die "Couldn't open damF.txt\n";
while (my $row = $csv->getline ($file2)) {
     next if ($.==1);
     my ($damID, $damF, $damAHC, $prog) = @$row; 
    if ($prog && ($hash1->{$prog})) {
       my $status = $csv->print($Output, [$prog,@{$hash1->{$prog}},$da
+mID,$damF,$damAHC]);
       print "\n";
       }
     }
close $file2;
print "Done";
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