Have you tried "hard wiring" the address (print MAIL "Reply-To: parent@hotmail.com\n";)?

If it still fails then that implies that sendmail is giving you grief. At that point you might like to investigate MIME::Lite:

use MIME::Lite;

$msg = MIME::Lite->new(
        From     => 'no-reply <webmaster@domain.org>',
        Reply-To => $efrom,
        To       => 'recipient@mailserver.com',
        Subject  => $esubject,
        Data     => $emessage,
        );

$msg->send;
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