Order entries, exclude 'the' from order criteria
Completely untested, but try something like this:

{% for entry in craft.entries.section('hotels').order('(CASE WHEN title LIKE 'The %' THEN SUBSTRING(title, 4) ELSE title END )') %}


MySQL's LTRIM isn't what you want because that just removes leading spaces.  SUBSTRING should do it, though.

Also, keep in mind this is a MySQL specific query.  If you ever planning on running on PostgreSQL (that the Craft 3 beta supports), it would have to be adjusted.