If what you say is directly from the SW lore, then you are effectively destroying your own argument.
Spartan community was anything but family-oriented. Weak and frail babies were discarded from birth, strong young men were taken by the army to train as a soldier for a period lasting almost a decade, never seeing their family until the return - if they survived the strict martial camps and harsh drills. Also, Spartans hardly fought to find glory, not to mention forming a workable state beyond Peloponnesus. The Spartan kleurochy system was a strict military-oriented tolitarian state, ruled by an olicargy. They favored war above everything else. In fact, it was customary for young Spartan males to ravage the countryside, hunt down helots(independent slaves) and practice war - inside their very own land. I don't think those traits resemble Mandalorians at all.
I agree that the martial prowess and strict form of Mandos may remind one of Spartans, but that's based on the romanticized image of them - as saviours of all Hellas during the 4th Century BBC. The reality was far more grim.
Just from "a historian" to another.