Maybe you are confused. "Este es mi hijo" isn't rude... when you refer to other people only with "este"... (this one), that is rude; or if you say something negative about the person.... "this one is lazy", "this one is like that", "this one doesn't work"; "este es flojo", "este es así", "este no trabaja".
"Ambos", never is rude.
This is interesting. It's the first time that I see two dictionaries disagree on a topic. The Oxford English Dictionary states that there are just two items involved. I would generally recommend using "all of" instead of "both" when talking about more than two things.
Anyway, the RAE definition of ambos parallels the OED definition nicely. It's two things.
They both is incorrect in English. I can't explain why but it just sounds wrong. sydnea02 probably got hers excepted because she used 'both are.' I used 'They are both my daughters' and it was just fine. You needed the 'are' in between or it just sounds funny and that's in English.