The bible teaches that we should submit to our governments in:
Romans 13:1-2 (KJV)
Let every soul be subject unto the higher powers. For there is no power but of God: the powers that be are ordained of God. Whosoever therefore resisteth the power, resisteth the ordinance of God: and they that resist shall receive to themselves damnation.
1 Peter 2:13-14 (KJV)
Submit yourselves to every ordinance of man for the Lord's sake: whether it be to the king, as supreme ; Or unto governors, as unto them that are sent by him for the punishment of evildoers, and for the praise of them that do well.
The Catholic church considers the Pope to be the Vicar of Christ
The traditional assertion of Catholics in this matter is that each pope has the totality and supremacy of the power Christ left on earth for the building up of the kingdom of God. The pope is said to have the plenitudo potestatis, or fullness of power. His authority, direct from Christ after the manner of a vicar, extends equally directly to each man, woman and child committed to his care, namely all men. This fact of papal primacy has been denied on numerous occasions, but chiefly in five great eras of the Church's history.
It should be observed in conclusion that papal infallibility is a personal and incommunicable charisma, which is not shared by any pontifical tribunal. It was promised directly to Peter, and to each of Peter's successors in the primacy, but not as a prerogative the exercise of which could be delegated to others. Hence doctrinal decisions or instructions issued by the Roman congregations, even when approved by the pope in the ordinary way, have no claim to be considered infallible. To be infallible they must be issued by the pope himself in his own name according to the conditions already mentioned as requisite for ex cathedra teaching.
Do the papal teachings supersede government rules where they conflict? Is there an historic precedence of either?
On the surface, it would be easy to say, "the Pope is the Vicars, he rules". But we must consider that historically the pope (the person, not the title) hasn't always been a good representation for the church, either because the wrong person was chosen or another reason. Which is why I'm looking for an historic precedence.