Dear @Andrey_Malk,
Welcome back to the Wefugees Community and sorry to hear about your struggles.
Georgia is considered by now as a so-called "safe country of origin" - please follow the link to see Handbook Germany's information on this as special regulations may apply. It is good to hear that you were allowed to work so far as the authorities usually don't give the permission for applicants from these so-called safe countries (they are usually not allowed to move out of the initial reception centres/to private housing either). In case your young son is not getting the permission to make a dual vocational training (Ausbildung), he may consider to start a school-based vocational training which doesn't require the authorities' permission.
I highly recommend you to get some individual advice at a specialised counselling office - the best would be the asylum procedure counselling (Asylverfahrensberatung) to assess your options. Someone needs to check your case as a whole - it is hardly possible to give serious legal advice based on very little information on this public platform. In general, for the §60d ("Beschäftigungsduldung") you need to be tolerated (holding a Duldung) for at least 12 months before being able to apply for it. I assume you are still holding an "Aufenthaltsgestattung", right?
All the best,
Meike