Hello,
first of all, it is difficult to give advice without knowing why your Ausländerbehörde wants to deport you and especially your son, separating you from your wife and, more important, the child from the mother.
Generally, your wife's Ausbildungsduldung doesn't give you and your son absolute right to stay, according to German law. But it is not very usual to separate a family which lives together, especially children from mother. It would be against the principle of child's wellfare which stands very high. Perhaps you got decisions from Ausländerbehörde with explanation (Begründung) why they consider it possible to deport you.
It is possible to make an urgent application against deportation in the court if you think that you are really in danger. But you normally need support from a good lawyer who specialises in Aliens law or at least from a good refugee councelling center in your place.
If you made an application for permission to make Ausbildung in a written form (officially), you have right for a written answer from Ausländerbehörde with the reasons for rejection. I can imagine that they reject because you only have A2 (normally you need at least B1 or even B2 to start a qualified Ausbildung which can bring you Ausbildungsduldung). Another reason can be that you ask for permission too early. The application for Ausbildungsduldung can be made earliest 7 months before your Ausbildung starts. I don't know if there is such a rule for giving a permission for Ausbildung. But perhaps they think it is too early. Unfortunately some Ausländerbehörden use the principle that deportation has priority if people don't have an absolute reason to stay.
Anyway, online councelling can't be enough if you need quick measures to prevent deportation. I hope, you can find personal support.