But the college or body of bishops has no authority unless it is understood together with the Roman Pontiff, the successor of Peter as its head. The pope's power of primacy over all, both pastors and faithful, remains whole and intact. In virtue of his office, that is as Vicar of Christ and pastor of the whole Church, the Roman Pontiff has full, supreme and universal power over the Church ... A council is never ecumenical unless it is confirmed or at least accepted as such by the successor of Peter; and it is prerogative of the Roman Pontiff to convoke these councils, to preside over them and to confirm them.[LG 22; emphasis added]The authority of a council can never be divorced from the the authority of the Pope.
the infallibility promised to the Church is also present in the body of bishops when, together with Peter's successor, they exercise the supreme Magisterium," above all in an Ecumenical Council [CCC §891; emphasis added].So let's step back and think about some conclusions we may infer from this. First: it is entirely possible for a council to err - but not an Ecumenical Council. No Catholic will find any "comfort," as it has been put, in a non-ecumenical council when it errs (though of course we approve truth wherever it may be found). Is it disappointing when a council errs? Of course it is. It's a tragedy. We may rightly consider it to be a scandal, inasmuch as it may lead Christians into error who do not carefully weigh its pronouncements against the teaching of the Church, or who ignore the warnings of the Magisterium with respect to such a council's errors. But the fact that this may happen is hardly a matter of "inconvenience," if by that is meant some notion that it poses difficulties for Catholic doctrine. It doesn't.
So, for example, when the Council of Constance claimed for itself an authority superior to the Pope's, it erred - and no Catholic is bound by such nonsense (and no such claims were ever approved by a Pope). In fact, as the Catholic Encyclopedia mentions, "From the fourteenth session, in which he convoked the council, it is considered by many with Phillips (Kirchenrecht, I, 256) a legitimate general council," but that which occurred beforehand is invalid; "in a papal consistory (10 March, 1418), Martin V rejected any right of appeal from the Apostolic See to a future council, and asserted the supreme authority of the Roman pontiff as Vicar of Jesus Christ on earth in all questions of Catholic Faith...In particular the famous five articles of the fifth session, establishing the supremacy of the council, never received papal confirmation" (ibid; see also Hughes, The Church in Crisis: A History of the General Councils, 325-1870, pp. 290-305).
Secondly, it's impossible for one Ecumenical Council to contradict another, precisely because Ecumenical Councils enjoy the charism of infallibility by virtue of their union with the Pope, the Vicar of Christ.
It is this Magisterium's task to preserve God's people from deviations and defections and to guarantee them the objective possibility of professing the true faith without error. Thus, the pastoral duty of the Magisterium is aimed at seeing to it that the People of God abides in the truth that liberates. To fulfill this service, Christ endowed the Church's shepherds with the charism of infallibility in matters of faith and morals. the exercise of this charism takes several forms: "The Roman Pontiff, head of the college of bishops, enjoys this infallibility in virtue of his office, when, as supreme pastor and teacher of all the faithful - who confirms his brethren in the faith he proclaims by a definitive act a doctrine pertaining to faith or morals.... the infallibility promised to the Church is also present in the body of bishops when, together with Peter's successor, they exercise the supreme Magisterium," above all in an Ecumenical Council. When the Church through its supreme Magisterium proposes a doctrine "for belief as being divinely revealed," and as the teaching of Christ, the definitions "must be adhered to with the obedience of faith." This infallibility extends as far as the deposit of divine Revelation itself [CCC §890-891]It ought to be obvious from what I've said that Catholics don't "trust" in councils per se. Rather, our confidence is in the goodness of God, that he will in fact preserve his Church from error by the means he has provided - the gift of infallibility working in the Pope and in the Bishops in communion with him. It's a ridiculous slander to say that our trust is in men. No. Our confidence is in God, and his goodness is expressed in the Church so that we may trust him through her.