Is the second contract considered legally valid, taking into account that the wife's father was one of the witnesses in the first contract, and that he was her representative (wali) in the second contract, and that the wife's guardian (wali) cannot be a witness?

The marriage contract conducted through your brother's agency on behalf of the bride's father is valid, because deputizing in marriage is permissible. The witnessing of your father and your other brother to the contract is valid according to the preponderant opinion; because the testimony of ascendants and descendants is prohibited if it is a testimony for a person out of fear of accusation. However, in a marriage contract, it is a testimony for and against him, so it is not prohibited. Therefore, your wife is under your conjugal bond, and there is no need to renew the contract.