Omega does have districts controlled by other forces, Aria and lesser gangs being among those. I leave it up to you what district you want to be in and who controls it, you could even control your own district if you like, though that has both advantages and disadvantages. (Advantages: A stronger base for yourself, an extra income source in the form of taxes. Disadvantage: You'll have to fend off other Omega factions trying to gain control of the district from time to time.)

Also you are perfectly allowed to have existing relations with the big three, and that specific spread is all good. For more information on dealing with them, there is a section dedicated to it in the OP under the 'So how will it all work' hider.