I want to be able to filter orders "pending" and "processing" at the same time (like the last option on the image).
How would I do that?
You can get processing and pending order from order collection like this
$objectManager = \Magento\Framework\App\ObjectManager::getInstance();
$orderCollectionFactory = $objectManager->create('Magento\Sales\Model\ResourceModel\Order\CollectionFactory')->create();
$orderCollection = $orderCollectionFactory
->addAttributeToSelect("*")
->addFieldToFilter('status', array('in' => array('processing','pending')))
->setOrder('created_at','desc');
echo "<pre>";
print_r($orderCollection->getData());
echo "</pre>";
Try to use factory method instead of Object Manager.
status
column code in question.