To start with, you could eliminate redundancies (as I've tried to demonstrate by refactoring your code), and encapsulate data dependencies in a data structure, to the degree possible (see my %parent_hash in my snippet), rather than if statements.

I have taken your code and put in my script it works the problem I am having is somehow it does not recognize who the parent is and give send it to $name.

 # store subparent for each parent
my %parent_hash = ( 'Father' => 'Mother',
                    'Mother' => 'Father' );

if (exists $parent_hash{$parent}) {
  my $sub_parent = $parent_hash{$parent};

  for my $col ( $parent, $sub_parent ) {
    my $sql = "select $col from Roster where User=?";

    my $rv = $dbh->selectcol_arrayref( $sql, undef, $user );
    if ( @$rv ) {  # any rows returned?
      $name = $rv->[0];  # take first one
      last;
    }
  }
}
foreach $date ( @volunteer_date ) {

        $sth = $dbh->prepare ("select distinct Volunteer from Voluntee
+r
                                where Volunteer = \'$name\'
                                and Date = \'$date\'");
        $sth->execute ();

my $chk = $sth->fetchrow_array;

#Verify the parent is not signed up.
    if ($chk eq $name){
        print $query->h1({-align=>'center'}, "You are already signed u
+p for this date: $date");
        } #end if statement
#process the information and update the schedule.
   else{
   $sth = $dbh->prepare ("select max(Number) from Volunteer
                                        where Date = '$date'
                                          and Volunteer = 'TBD'");
   $sth->execute ();
   my $number = $sth->fetchrow_array;
   $sth = $dbh->prepare ("update Volunteer set Volunteer = '$name'
                       where Date = '$date'
                       and Volunteer = 'TBD'
                       and Number = $number
                                         ");
       $sth->execute ();
        print $query->h1({-align=>'center'}, "You signed up for this d
+ate $date")
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