How do I programmatically add an image while programmatically creating nodes?

May be not exactly what you need, but why not just add a reference to an image in a field, like your example 2 suggests ? And then in content template file render that field as an image.

In node creation stream:

$node->field_image['und'][0]['value'] = "/path_to_image/image.jpg";

In content type:

<?php
global $base_url;
$image_source_link=$base_url . $node->field_image['und'][0]['value'];
?>
<img src="<?php print($image_source_link); ?>" />

Let suppose your image fields in field_body_images ,

first load your node by node_load and record your image in file tables and add it to your node image field I hope this sample help you to achieve :

$n=  node_load($nid);
$file = new stdClass();      
$file->filename =$file_name;
$file->filemime =file_get_mimetype($localimagepath.$file_name);
$file->filesize = @filesize(file_create_path($localimagepath.$file_name));
$file->uid = $user->uid;
$file->status = 1;
$file->timestamp = time();
$file->list=1;
$file->data=array('alt'=>'','title'=>$n->title);
drupal_write_record('files', $file);
$record->fid=$file->fid;
$n->field_body_images[]=(array)$file;
node_save($n);