I've just been thinking that if verb + なさい constructions are a combination of verb stem + なさる's 命令形, how on earth is something like しなさい possible. they both mean "do", don't they ("do do!) perhaps I'm completely over-thinking this. Is there a reason as to why なさい can't be used its own?
The suffix なさい does not function like the verb なさる ("to do").
So to me, the なさい in しなさい is unrelated to "to do", it simply converts する into an imperative. (If you don't buy that a form of なさる can perform as a purely grammatical element, consider what function the "do" in "I do not know" is performing.)
Regarding the construction 漢語名詞＋なさい (e.g., 結婚なさい), it is productive, and according to @TokyoNagoyaさん, it seems to have a different, slightly softer connotation than the 〜しなさい construction. I am not sure where exactly it falls on politeness spectrum of the various different imperatives (〜しろ、〜して、〜してくれ、〜してください、〜しなさい、〜なさい, etc.）.
Personally I'd avoid trying to do some deep grammatical analysis of this. Perhaps someone else can chime in on the historical and etymological aspects.
We simply say やめなさい or おすわりなさい. It was one of the first grammatical forms I learned after getting married to a Japanese woman. :-) These can be viewed as informal variants of やめてください or すわってください or おすわりください. It's simply the grammatical rule that the なさい is preceded by the 体言止め form such as やめ or すわり, which in the case of する is し. So yes, it's お掃除しなさい, for example.