I'm no expert in this subject but here's a XSLT transform from the original XML into one with the correct order

#!perl
use strict;
use XML::LibXSLT;
use XML::LibXML;

=head1 test.xsl
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Tr
+ansform">
  <xsl:output indent="yes"/>
  <xsl:strip-space elements="*"/>

  <xsl:template match="node()|@*">
    <xsl:copy>
      <xsl:apply-templates select="node()|@*"/>
    </xsl:copy>
  </xsl:template>

  <xsl:template match="TRGROUP">
      <xsl:copy>
        <xsl:apply-templates select="COLS"/>
        <xsl:apply-templates select="COLSPEC"/>
        <xsl:apply-templates select="THEAD"/>
        <xsl:apply-templates select="TBODY"/>
      </xsl:copy>      
  </xsl:template>
</xsl:stylesheet>
=cut

my $parser = XML::LibXML->new();
my $xslt   = XML::LibXSLT->new();
my $stylesheet = $xslt->parse_stylesheet_file('test.xsl');

my $xml;
{
  local $/='';
  $xml = <DATA>;
}

my $source_doc = $parser->parse_string( $xml );
my $result = $stylesheet->transform( $source_doc );
print $stylesheet->output_string( $result );


__DATA__
<TABLE>
<TRGROUP>
  <COLS>AA</COLS>
  <TBODY>A</TBODY>
  <COLSPEC>XX</COLSPEC>
  <THEAD>1</THEAD>
</TRGROUP>
<TRGROUP>
  <COLSPEC>XX</COLSPEC>
  <TBODY>B</TBODY>
  <THEAD>2</THEAD>
  <COLS>BB</COLS>
</TRGROUP>
<TRGROUP>
  <TBODY>C</TBODY>
  <COLS>CC</COLS>
  <COLSPEC>ZZ</COLSPEC>
  <THEAD>3</THEAD>
</TRGROUP>
</TABLE>
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