I would think the Cadians would be something like IDF and that depicted in Starship Troopers (the movie). Yes, women would be part of it, and yes they would fraternize as hell, as we need to breed new strong soldiers. Even Hitler wanted his soldiers to breed in WW2, as long as they were "genetically acceptable" - special homes were set up to provide for such.
However the mother-child nurturing as seen in feudal societies and our own pre-suffrage society would be too inefficient - every Cadian should know how to field strip a lasgun before he can barely walk, so what better way to do this than through mass kindergartens? Maybe a young mother (40s and 50s mothers are more likely to breed genetically faulty children) would have a year of leave when she gets pregnant, but after the first weaning period the baby would be raised by semi-militaristic kindergartens, that seamlessly turn into Basic training and advanced training as the child gets older.
Every Cadian is a soldier first, and a civilian second. It still needs a lot of the latter - to produce goods, repair vehicles, etc. Thus only the best become Cadian shock troops and even their support elements, while the rest are defending the homeworld part-time.
Well, that's my take on it at least