Retrieve hidden field value & expose to .tpl file
That could potentially break and it's pretty gnarly looking, so not the best, but I've been there!

Instead if you have the field_collection_item's ID you can do:

// I'd make a more meaningful name... like slider?
// If I understand your example, this should give you the entity Object for the field_collection_item
$entity = array_shift($items[0]["entity"]["field_collection_item"]);

$field_image_data = field_get_items('field_collection_item', $entity, 'field_image');
// I'm less sure here, it looks like the image is an entity and it has sub-fields?
// You'll probably have to dig through $image to see where the entity is kept, I'm guessing
$field_alignment_data = field_get_items('file?', $field_image_data[0]['#entity'], 'field_alignment');

// Now you should be at your field
// If safe_value exists, use that.
$alignment = $field_alignment_data[0]['value'];


This is annoying, but more legible. It's what happens when you have nested data objects, things just get kind of annoying.

The other option is you could make it a field that isn't hidden and use hide('field_alignment') in the tpl.php or template_preprocess_* function (guessing it'd be template_preprocess_entity?)