Were you looking for a "non-Catholic take" on the issue of infallibility? Any non-Catholic by definition would reject that teaching. If there's a non-Catholic out there who believes in papal infallibility, they should convert to Catholicism. Something to prayerfully keep in mind if you yourself are struggling with that particular teaching is that the First Vatican Council anathematizes any Catholic who rejects it. As such I'm not sure how any Catholic who takes their faith seriously can deny that teaching and still call themselves Catholic or believe that Catholicism is the true church.
As for Amoris Laetitia - it is not an infallible document strictly speaking, but it is a magisterial document and must be read within the context of what the Catholic church teaches about the papacy. Many traditionalists and conservatives, led by the likes of Cardinal Burke, are trying to convince themselves and others that it is not so because of the implications that necessarily follow. However, when one recalls that Pope Francis himself said that his interviews were part of his official papal magisterium and had the Vatican's printing office print them as such, it's frankly absurd to suggest that an apostolic exhortation written at the conclusion of two church synods is somehow not magisterial.
That said remember what Catholicism teaches about the papacy which from a Catholic perspective is infallible. The two most recent (supposedly) ecumenical councils - Vaticans I and II - state the following:
"Wherefore we teach and declare that, by divine ordinance, the Roman Church possesses a pre-eminence of ordinary power over every other Church, and that this jurisdictional power of the Roman Pontiff is both episcopal and immediate. Both clergy and faithful, of whatever rite and dignity, both singly and collectively, are bound to submit to this power by the duty of hierarchical subordination and true obedience, and this not only in matters concerning faith and morals, but also in those which regard the discipline and government of the Church throughout the world." - Pastor Aeternus
"Religious submission of mind and will must be shown in a special way to the authentic magisterium of the Roman Pontiff, even when he is not speaking ex cathedra; that is, it must be shown in such a way that his supreme magisterium is acknowledged with reverence, the judgments made by him are sincerely adhered to, according to his manifest mind and will." - Lumen Gentium
The issue of divorce, remarriage, and communion is certainly one of faith, morals, and discipline, and Amoris Laetitia, while not ex cathedra, requires the reverential obedience of the Catholic faithful assuming that the above teachings are true.
When I was in the seminary we had a professor who repeatedly stressed to us that God gave us both faith and reason and that we could not rely on one to the exclusion of the other. These issues have to be looked at not just with faith but with reason as well. You mention logic - when you boil it all down - here are your only logical, reasonable options:
1. What the Catholic church teaches about the papacy is true and Francis is truly the pope. However, what that means, as we are discovering, is that moral truth is not objective but subjective. That's what Jesus meant in the passage in Matthew's gospel where he bestows the keys on Saint Peter, that what was once bound on earth can now be loosed. Today, it's the definition of adultery, tomorrow it's homosexuality or abortion or who knows what, and a pope can contradict his predecessors and/or the teachings of councils because he holds the keys and has that power.
2. What the Catholic church teaches about the papacy is true but Francis is not really pope. That will lead you to sedevacantism in some form - either the traditional "there hasn't been a real pope since Pius XII" version espoused by people like those on the website Novus Ordo Watch or the seemingly growing "resignationist" version where the resignation of Benedict XVI was invalid and therefore he's still pope and Francis is not. To accept that you have to believe that the 99.99% of the world which thinks that Francis is pope is wrong and that includes Benedict himself who recognizes the reality of Francis' papacy.
3. Francis is pope, but what Catholicism teaches about the papacy is false which leads to Orthodoxy.
Some people are trying to construct for themselves a false middle ground. The so-called "recognize and resist" option, popular among traditionalists that often leads its proponents to parishes run by traditional orders like the Fraternity of Saint Peter, or to the newly created Ordinariate, or to Eastern rite Catholic churches. But a better, more reverent liturgy, is really just a placebo for such individuals, an effort to escape from reality rather than confront it. All such groups are under the full authority of Pope Francis and in full communion with the church in Malta which, largely based on Amoris Laetitia, just approved communion for those divorced and civilly remarried Catholics who are "at peace" with the choices they have made, rejecting the explicit and "infallible" doctrine of the Catholic church.
Religion, like politics, involves A LOT of emotion, but I hope that you will be able to put some of that aside and prayerfully look at these matters with logic and reason. A crisis of faith, although painful and traumatic, can be a great blessing in the end if it leads you to the truth. May God bless you and guide you in your journey.