How to sync a taxonomy between Drupal and a 3rd-party system?
You can import taxonomies, and even nested taxonomies, with CSV data generated from your source data. I have been done before and it works quite well with module Feeds.

As for your taxonomy system, you must generate dynamical CSV files (in fact, a PHP or a Drupal node with some custom code), which feeds the Imports you generate in Drupal and which are associated to a vocabulary. In that way you can generate taxonomies with children.