Order by custom field in query multiple

You need 'order_by' => 'post__in' in the last query in order to “Preserve post ID order given in the post__in array (available with Version 3.5).”.

I don’t know if the order you are passing in is the order you want after the array_merge( $group_1, $group_2). In other words, you need to feed that second query an ordered set of IDs and you don’t seem to be doing that.

I also can’t tell if one or the meta_keys you’ve already queried is what you want to orderby. Possibly something like this will work:

$the_query = new WP_Query(
    array(
        'post__in' => array_merge( $group_1, $group_2),
        'meta_key' => 'your_date_field_key',
        'orderby'  => 'meta_value',
    )
);

That is completely untested. Possibly buggy. Caveat emptor. No refunds.