Email copy of shipment checkbox can be disabled from configuration.
Looking in the template that renders that section you will see this:
<?php if ($this->canSendShipmentEmail()): ?>
<label class="normal" for="send_email"><?php echo Mage::helper('sales')->__('Email Copy of Shipment') ?></label>
<input id="send_email" name="shipment[send_email]" value="1" type="checkbox" />
<?php endif; ?>
This means that the checkbox is shown only if
$this->canSendShipmentEmail() evaluates to
Going deeper on this you will see that the config path
sales_email/shipment/enabled determines if it's allowed or not.
The value for that config path can be changed from
Set that to
Yes and you will see the checkbox in your other website.