Notice Successor of Peter and "Lineal succession".
The only time that the antiCatholics invoke Augustine is when they think that they have a gotcha moment against Catholicism. Or in a mistaken defence of Calvin's hellish doctrines.
It doesn't matter that Augustine was declared a Saint of the Church. Just as St. Paul is routinely misinterpreted and used to develop personal doctrine, so is Augustine. The rubble of the Reformation and the ruin of the Restoration demands no less.
RE: I would not believe in the Gospel, if the authority of the Catholic Church did not move me to do so.
Scripture itself and the Holy Spirit, who guides people in the truth moved me to believe in the Gospel. The church played a role true, bit it does not necessarily be limited to the Roman Catholic Church.