Imam Hussein enjoys a very high station near Allah and traditions are narrated that the dust around his sanctuary will cure all illnesses., These include the deseases of the soul as well as the body.
This blessed Turbah should be greatly respected and special ettiqutte should be followed to achieve maximum benefit from it.
The right way is to just take very little of it and mix it with as much water as you like, and you can benefit from reciting the dua before consuming it too even in his absence before he takes it.
Every action done with a sincere intention will certainly have its positive effect. Therefore, if you yearn for your sons guidance and give him the water without his knowledge, it will inshAllah cure him.
However, some scholar's have the opinion that if one doesn't have the love of Imam Hussein in his heart or doesn't have faith on his intercession even in this world, he will not get its benefit. There should be a respect for the beloved Imam for any result to be shown, be it in the presence of the one who is ill or even in his absence.
Many non Muslims have known to be cured by the miraculous turbah and although they didn't have faith in the religion of Allah, however they carried a respect in their hearts for Imam Hussein a.s.
Thus, if you can try to inculcate this love and respect of Ahl bayt a.s in your son's heart then inshAllah he will change even before taking the Turbah.
In any case, you have guardianship over your son since you have the honour of being his mother so you can do the best that you know will carry its positive effect.
Know that a mothers prayer for her child reaches acceptance so you have to do your best in all ways then leave the rest on Allah.
Allah finds excuses to guide and forgive His servants so you need not worry after trying your best and persisting in the best way possible.