It looks to me like you are ordering your query in the wrong place, but without knowing what your expected output is, this is a guess at what you $sql2 query should be:
SELECT client.* from client where parent_client_id = '1234' JOIN extension on extension.client_id = client.client_id ORDER BY FIELD(extension.type, 'term', 'queue', 'ivr', 'voicecentre', 'conference', 'callback', 'intercom', 'queuecentre')
Also - PLEASE note the comment by @tadman and use
mysqli and properly escape your data.