So what you do is when the link is clicked the onclick() event is fired, a new popup window opens loading the print.php script ( return popitup('print.php') ), and the link never redirects the page to the actual print.php with correct print parameters, right?
Why do you need a popup at all? Maybe I don't get it, but I think you should be fine with only of of them, either:
<a href="#" onclick="return popitup('print.php&order=<?php echo $rand_str; ?>')">Print this record</a> || <a href="?cid=home">Continue</a>
OR
<a href="print.php&order=<?php echo $rand_str; ?>">Print this record</a> || <a href="?cid=home">Continue</a>