"... and it outputs an XML file with the apostrophes and quotation marks intact."

The source for XML::Writer has this routine defined:

sub _escapeLiteral {
  my $data = $_[0];
  if ($data =~ /[\&\<\>\"]/) {
    $data =~ s/\&/\&amp\;/g;
    $data =~ s/\</\&lt\;/g;
    $data =~ s/\>/\&gt\;/g;
    $data =~ s/\"/\&quot\;/g;
  }
  return $data;
}
[download]

Here is the code that i used:

use strict;
use warnings;
use XML::Writer;

my %hash = (
    str1 => 'one<two',
    str2 => 'one&two',
    str3 => 'two>one',
    str4 => 'Caisse D"Eparge',
    str5 => q(Caisse D'Eparge),
);

my $Writer = XML::Writer->new(
    OUTPUT      => 'self',
    DATA_MODE   => 1,
    DATA_INDENT => 2,
);

$Writer->startTag('root');
$Writer->dataElement( $_, $hash{$_} ) for sort keys %hash;
$Writer->endTag('root');
$Writer->end();

print $Writer->to_string;
[download]

<root>
  <str1>one&lt;two</str1>
  <str2>one&amp;two</str2>
  <str3>two&gt;one</str3>
  <str4>Caisse D"Eparge</str4>
  <str5>Caisse D'Eparge</str5>
</root>
[download]

I would recommend using another XML module, perhaps even recommend using JSON instead if possible.

L-LL-L--L-LL-L--L-LL-L--
-R--R-RR-R--R-RR-R--R-RR
B--B--B--B--B--B--B--B--
H---H---H---H---H---H---
(the triplet paradiddle with high-hat)