(a) transfer of case from one state to another can be permitted by the Supreme Court of India. you may need to file a TRANSFER PETITION before the Hon'ble Supreme Court.

(b) the Bangalore family court cannot transfer the case. however, you may seek adjournment for filing transfer petition.

It is better to file the Transfer case well ahead of the hearing in the Bangalore case.

Supreme Court Legal Aid is available for those who cannot afford the expenses.

You may have to appear personally in the Bangalore court without lawyer's presence and say that your transfer case is filed in Supreme Court.

you simply have to fiel a transfer petition in the supreme court of india and the court would stay the proceedings of the case at bangalore and later transfer the case to delhi/noida as per your desire. merely sending a letter to the court in bangalore would be of no use.