Does the Traditionalist and Sedevacantist ignore the words of St.Ambrose saying "Ubi Petrus, Ibi Ecclesia, Ibi Deus"? The above Latin quote, attributed to St. Ambrose means “Where Peter is, there is the Church, there is God.”

According to the Catechism of the Catholic Church (CCC), Jesus “entrusted a specific authority to Peter”:

Simon Peter holds the first place in the college of the Twelve; Jesus entrusted a unique mission to him. Through a revelation from the Father, Peter had confessed: “You are the Christ, the Son of the living God.” Our Lord then declared to him: “You are Peter, and on this rock I will build my Church, and the gates of Hades will not prevail against it.” Christ, the “living stone,” thus assures his Church, built on Peter, of victory over the powers of death. Because of the faith he confessed Peter will remain the unshakeable rock of the Church. His mission will be to keep this faith from every lapse and to strengthen his brothers in it.
Jesus entrusted a specific authority to Peter: “I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven.” The “power of the keys” designates authority to govern the house of God, which is the Church. Jesus, the Good Shepherd, confirmed this mandate after his Resurrection: “Feed my sheep.” The power to “bind and loose” connotes the authority to absolve sins, to pronounce doctrinal judgments, and to make disciplinary decisions in the Church. Jesus entrusted this authority to the Church through the ministry of the apostles and in particular through the ministry of Peter, the only one to whom he specifically entrusted the keys of the kingdom. (CCC 552-553)

The Daily Roman Missal has this to say about the feast of The Chair of St. Peter:


  This feast brings to mind the mission of teacher and pastor conferred by Christ on Peter, and continued in an unbroken line down to the present Pope. We celebrate the unity of the Church, founded upon the Apostle, and renew our assent to the Magisterium of the Roman Pontiff, extended both to truths which are solemnly defined ex cathedra, and to all the acts of the ordinary Magisterium. (pg. 1485) - “Ubi Petrus, Ibi Ecclesia, Ibi Deus”


Cardinal Caffara also had a statement of support reminding all the Bishops to not contradict the Pope;

«I was born Papist, I lived as a Papist, and I mean to die a Papist! If a Bishop has a thought contrary to that of the Pope» – he concluded: «he must go away, but really he must go away from the diocese. Because he would lead the faithful into a path that is not the one of Jesus Christ anymore. Therefore, he would lose himself eternally and would risk the eternal loss of the faithful». - Card. Caffarra: «Let who is against the Pope go away; he will lose himself»
I can't answer for traditionalists who are not sedevacantists, but for sedevacantists there is no problem here. When there is a pope, we will follow him. I don't think your quotation from St. Ambrose was intended to imply that, during periods when there is no pope, the church and God disappear. (There have often been periods without a pope.  Until recently, they were caused not by heresy but by the death or resignation of a pope.)