Unless the external site is on the same server as your plugin, there is no reliable-yet-simple way to obtain the information you want. The best you can do is run the following query:
SHOW TABLES LIKE '%term_taxonomy%'and if it returns just one row, you can parse the result to get the table prefix. If it returns multiple rows, the database contains multiple WordPress installations (multisite), and things get much more difficult. At that point you'll need to read data from each _options table (using the prefixes you parsed above) and hopefully find something which matches information you have locally.
