Your father started company with your brother - what does it mean? Is it not a Partnership? OR your father is the sole proprietor of the said concern. (If so, your brother is not having any right over the concern).
Any proprietory concern is nothing but a personal business of an individual. He can always call for another person to join and convert the same into a Partnership Business.
Better check with the concerned Bank, if they can change the name of the account from your father's name to Firm's name upon producing Partnerhsip Deed with Registration Certificate, and new specimen cards of all the Partners.