Admittedly I've been looking heavily at the Imperial Megacorporation in Warzone/Mutant Chronicles.
Granted, that was Corporations that evolved into Clans with one each specialising in certain industries (ie, arms manufacturing, brewing, astro-mining, etc).
Affiliated Houses and families would probably find it easier finding work in the sector that their parent Clan focuses on, but it wouldn't be difficult to find work elsewhere especially if specialist workers are required.
Stated already that the upper house of the Commonwealth parliament is made up of representatives from the various clans, whereas the lower house is like our House of Commons and thus filled with elected MPs. With the Clans specialising in certain industries they tend to have a bit of clout where these industries are located and thus have 'favoured' candidates when it comes to elections that affiliated members are encouraged to vote for. This can give Clans influence in both houses, also provides power blocs mirror each other in both houses.
Alyeska has its own, though much reduced, parliament along similar lines to a Dominion state of the British Empire. Its parliament will probably only contain a single chamber. And yeah, it doesn't send any reps to the CW's main parliament.