First of all, I want to say that I am not a lawyer, but I have worked, many years ago, with Italian citizenship processes, so I believe I can help you.
I am a Brazilian citizen and I live close to the city of São Paulo.
I would like to know which city the mother and the son are in and the consulate they are looking for.
Regarding the tests, were they performed with official translators?
If you have any questions, please contact me.