Call the new faction BAF. (Which would make a hell of a lot more sense than QCO/QCP OR SF)
Bretonian Armed Forces.
No bizarre sub-factions.
Carina, Regina, Imperatrix.
I agree here, to a point.
I would use the 66th model as inspiration here. QCO/QCP would be the assault force and dirty brigands, much like 202nd. SF (probably needing a rename) would take the honoured position as BAF Guard, keeping the position as the 'old officers club' that the QCO aren't fans of. This will make the faction unified whilst maintaining RP rivalry.
Of course, should the guards be in a sticky position, the assault fleet could return to aid them, and should additional punch be needed, the Guard could join with the assault fleet.