You may find XML::TreeBuilder more suited to your task:

use warnings;
use strict;
use XML::TreeBuilder;

my $str = <<'STR';
<dataschemas>
  <dataschema name="varyingName1">
    <attributes>
      <attribute>
      attr 1
      attr 2
      </attribute>
    </attributes>
  </dataschema>
  <dataschema name="varyingName2">
   <attributes>
    <attribute>
    attr 1
    attr 3
    </attribute>
   </attributes>
  </dataschema>
</dataschemas>
STR

my $xml = XML::TreeBuilder->new;
$xml->parse($str);

my @attributes = $xml->find('attribute');
for (@attributes) {
    # Figure out where the element is
    my @lineage = reverse $_->lineage ();
    my @eNames =
        map {$_->tag() . ($_->attr('name') ? '(' . $_->attr('name') . 
+')' : '')}
        @lineage;
    
    print join ('/', @eNames), ":\n";
    
    # Access the element text
    my $oldText = $_->as_text();
    print "$oldText\n";

    # Alter the content
    $_->push_content ("Extra attribute added");
}

print $xml->as_HTML ('<>&', '  '); # Looks bogus, but gets indentation
[download]

Prints:

dataschemas/dataschema(varyingName1)/attributes:

      attr 1
      attr 2
      
dataschemas/dataschema(varyingName2)/attributes:

    attr 1
    attr 3
    
<dataschemas>
  <dataschema name="varyingName1">
    <attributes>
      <attribute>
      attr 1
      attr 2
      Extra attribute added</attribute>
    </attributes>
  </dataschema>
  <dataschema name="varyingName2">
   <attributes>
    <attribute>
    attr 1
    attr 3
    Extra attribute added</attribute>
   </attributes>
  </dataschema>
</dataschemas>
[download]

Update: added editing sample code