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If you have a Duldung (suspension of deportation) you might be eligible for a so called "Ausbildungsduldung". It basically means that if you find a vocational training (Ausbildung) in Germany that fulfills several conditions, you will get the allowance to stay in Germany for the duration of your Ausbildung and after that you are eligible for a permit of residence to work. This Ausbildung could take place anywhere in Germany and you would normally be allowed to move there. Your family in this case would most likely also be allowed to move with you (but this depends on their status as well). Still it would be important that you don´t just move but ask for it at the immigration office (Ausländerbehörde) and wait for formal permission to do so.
On this page you find more information about Ausbildungsduldung and the requierements:
If you want to apply for Ausbildungsduldung it would be best for you to find a local counselling centre. There are many of those that offer free help, you can find one close to you via one of this pages:
I hope I could help you with this information. Since I don´t know many details of your case this might not be the only option for you/ there might be alternatives. So please don´t hesitate to ask if you have more questions about this topic!