Try this... Have your form POST the info to a page on your site that looks something like this:
$formValue1 = $_POST['formvalue1'];
$formValue2 = $_POST['formvalue2'];
$formValue3 = $_POST['formvalue3'];
$message = "value1: $formValue1\nvalue2: $formValue2\nvalue3: $formValue3";
mail("Your_Email_Address", "Subject", "$message");
$page = "<html>
<head>
<stuff>
</stuff>
<script type='text/javascript'><!--
function submitForm()
{document.forms['formName'].submit();
}
// --></script>
</head>
<body onLoad='submitForm();' bgcolor='#ffffff'>
<form action='pageOnOtherServer.php' method='POST' name='formName' target='_blank'>
<input type='hidden' name='formValue1' value='$formValue1'>
<input type='hidden' name='formValue2' value='$formValue2'>
<input type='hidden' name='formValue3' value='$formValue3'>
</form>
<moreBodyStuff>
</moreBodyStuff>
</body>
</html>';
echo $page;
This page could contain anything you want, but if it contained a form with hidden fields, that you could have PHP set the values of the fields, and have JavaScript submit the form onLoad. If you specify a new window as the target of the form, then whatever happens on the other server will happen in the new window, and your page can keep loading...
Does that help?