I specifically told my attorney not to correspond or respond to my brother on any further issues, since the dispute we had was resolved. Do I have the right not to pay the bill since I gave them strict orders not to correspond or respond to him.
DUI / DWI Attorney
If this is what you specifically said to your lawyer, then he is not following your explicit instructions and you should dispute your bill. You should do so in writing so there is a paper trail proving that you voiced your objections. Do not pay the bill until it is resolved.
Family Law Attorney
Will you be holding your attorney responsible if the attorney fails to act on something that is in the brother's emails?
While clients have the right to set the broad objectives of the representation, attorneys generally have the rights to determine how to achieve those objectives. Personally, I would stop working for any client that tries to micromanage me by directing whose emails I will read.
You can check into whether you can ask the court to order your brother to pay the attorney's fees needed to respond to whatever email your brother sent.