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Are you currently living in a camp (Gemeinschaftsunterkunft)? If so, it is usually possible to change your place of residence in the same city, in some states of Germany it is even possible to change your city inside the same region (Landkreis). However, for that you need to apply for a permission in your Social Affairs Office (Sozialamt) or in some states you need to apply in your Foreigners' Office (Ausländerbehörde) for that.
The social workers in your camp will give you information about it, where you should apply for that. They will also help you write an application for it.
After getting the permission and moving to the apartment with your family, you should inform your lawyer, your respective Foreigners' Office and the Federal Office for Migration and Refugees of Germany (BAMF) about your new address, as soon as possible.