Unfortunately, without more facts, I have to give you the Typical Lawyer Answer which is: "yes, and no."
If your brother wasn't authorized either as a co-signer or authorized user
of the credit card, your father wouldn't be held responsible for improper use of the card by someone who isn't permitted to use the credit card. If that is the situation, your father should report the improper use of the card as soon as possible to the credit card company and dispute the charges.
If, however, your brother was a co-signer or authorized user of the card, he would've been within his rights to use the card for any legitimate purpose -- and whomever is listed as a responsible party on the credit card would have the obligation to make payments. Even if your brother is permitted to use the card, he may be responsible to pay your father back for payments your father is required to make to the credit card company.
However, enforcing this obligation may be somewhat problematic for your father both in terms of family dynamics and your brother's ability to repay your father.