US courts recognize Sharia Law if a Muslim couple divorces; they recognize Torah law if a Jewish couple divorces. Yet, in a divorce involving Catholics, the US Courts do not recognize Canon Law.
Here is a link to the brief filed by Marie “Bai” MacFarlane’s in 2004, arguing that a marriage in the Catholic church is an inherent prenuptial (or “antenuptial”) agreement in which the parties agree to abide by the Church’s law concerning divorce, so no-fault divorce is impossible for a couple married in the Catholic Church. Sadly, we know how this turned out for MacFarlane.
5. The teachings of the canon law of the Church, specifically Canon 1153 and Canon 1692, states the following regarding separation:
Can. 1153 [more Catholic commentary (transcriber’s note)]— §1. A spouse who occasions grave danger of soul or body to the other or to the children, or otherwise makes the common life unduly difficult, provides the other spouse with a lawful reason to leave, either by a decree of the local Ordinary or, if there is danger in delay, even on his or her own authority. §2. In all cases, when the reason for separation ceases, the common conjugal life is to be restored unless otherwise provided by ecclesiastical authority
Can. 1692 — § 1. Unless lawfully provided otherwise in particular places, the personal separation of baptized spouses can be decided by a decree of the diocesan Bishop or by the judgement of a judge in accordance with the following canons. §2. Where the ecclesiastical decision does not provide civil effects, or if it is foreseen that there will be a civil judgement not contrary to the divine law, the Bishop of the diocese in which the spouses are living can, in the light of their particular circumstances, give them permission to approach the civil courts. § 3. If the case is also concerned with the merely civil effects of marriage, the judge is to endeavor, without prejudice to the provision of § 2, to have the case brought before the civil court from the very beginning.