No, the government's most important (and, properly, sole) job is maintaining the peace by suppressing assault and fraud and adjudicating disputes in the absence of other resolution. Permitting it to select and enforce a "right order" over and above that is the route to utopian totalitarianism.
(Oh, and what's with the capitalization? I can't find anything in the list of noun capitalization rules to account for it, unless "Government" is the deity you worship -- which would be the natural corrolary to believing that it has the secret to the "right order".)
You've done a reasonable job of defining Right Order.
Learn capitalization rules on your own.