Facepalm with me
Federation seems oddly deffensive don't they? Gasp!
Could it be they aren't as good as they think they are! 
Good one on the Alliance for hitting the Federations ego that badly.
If anything it's the complete opposite. The Federation is heavily outnumbered 2 to 4 if you only take into account the number of factions and don't consider player base. If you include player base, the Federation is even worse off.
Mahon helps whatever side is the most beneficial to him at the time. He gets attacked by the Empire, he sides with the Federation. He get's attacked by the Federation, he sides with the Empire. We can clearly see how strong his moral fiber is.
If you take into account recent events, it's pretty outstanding where Hudson sits right now considering he not only beat the Empire through military action, but also beat Mahon through economics.
Alliance was once under both Imperial and Federal control, there was a war in the HQ of the Allaince with the Thargoids but the people of the system got fed up with both the Imps and Feds going in doing whatever the hell they want so the Alliance was formed and fought of both the Empire and Feds and alligned with the Thargoids.
And your history is wrong. The Thargoid invasion officially began in 3055 and was initially fended off by the GalCop Navy. By 3123 GalCop was replaced by the INRA Attack Wing after repeated failed attempts of holding back the Thargoids. The INRA, a joint venture between the Empire and Federation originally founded in 2900, defeated the Thargoids after the introduction of the Mycoid Virus in 3193.
The Alioth Uprising, or birth of the Alliance, did not happen until 3230.
And out of curiosity, do you even have any idea why there was/is conflict between the Federation and Empire?
