1. No you need not take back or withdraw the earlier complaint. Both the cases can proceed simultaneously.
2. If the CAW Cell is not acting on your complaint then you have to move an application in the court of Magistrate so the court may direct the local Police Station to register FIR on the basis of your complaint and make proceed with necessary investigation.
3. The DV case filed by your mother needs to be perused. If allegations are of self same nature and in it abuses on you was also mentioned then you need not file separate DV case.
4. Otherwise do file a DV case and pray for his ouster from the shared household along with other necessary releifs.