Magento – Send Specific Email Depending On Payment Method (i.e. to include Bank Details)

Var $payment_html is injected in email variables in Mage_Sales_Model_Order::sendNewOrderEmail() and not available for update emails. Since exact block wich is rendered depends on payment method you will need to get that HTML using same way as in Mage_Sales_Model_Order::sendNewOrderEmail(). You can either extend and overwrite Mage_Sales_Model_Order::sendNewOrderEmail() or create your own block and reference it in the email template.

{{block type="your/block_type"}}

The only problem is how to pass order to your block. I am not sure if var order will work in this context.

If you want the email to be sent in all the cases remove make the code look like this:

$redirectUrl = $this->getQuote()->getPayment()->getOrderPlaceRedirectUrl(); 
if ($order->getCanSendNewEmailFlag()) { 
    try { 
        $order->sendNewOrderEmail(); 
    } catch (Exception $e) { 
        Mage::logException($e); 
    } 
}

But I don't think it's a good idea. This way the customer will receive a confirmation of his order before he actually pays. A clean solution would be to leave the code as it originally was and for the credit card method send the e-mail when the payment confirmation comes back from the card processor.