I know you've said you use XML::Twig, but ... this solution has the additional advantage that it doesn't keep the whole parsed document in memory:

use strict;
use warnings;
no warnings 'uninitialized';
use XML::Rules;

my $xmlStr = <<XML;
<foo>
    <qp name="foo">
        <q supp="yes">hello</q>
        <q supp="no">bye</q>
        <xr supp="yes">later</xr>
    </qp>
    <qp name="bar">
        <q supp="yes">bye</q>
        <xr supp="no">later</xr>
        <xr supp="no">sometime</xr>
    </qp>
</foo>
XML

my $parser = XML::Rules->new(
    stripspaces => 7,
    rules => {
        'q,xr' => sub {
            return if $_[1]->{supp} eq 'yes' or $_[1]->{info} eq 'yes'
+;
            return '+count' => 1;
        },
        qp => sub {
            printf "Definition '%s' has %d quotations.\n", $_[1]->{nam
+e}, $_[1]->{count}+0;
            return '+total' => $_[1]->{count}+0;
        },
        foo => sub { return $_[1]->{total} },
        _default => '',
    },
);

my $total = $parser->parse($xmlStr);
print "The total count is $total\n";
[download]