Mrs. MacFalane is not entirely correct.
Canon 1152 §1: Although it is earnestly recommended that a spouse, moved by Christian charity and concerned for the good of the family, no refuse forgiveness to an adulterous partner and not disrupt conjugal life, nevertheless, if the spouse did not condone the fault of the other expressly or tacitly, the spouse has the right to sever conjugal living unless the spouse consented to the adultery, gave cause for it, or also committed adultery.
And my commentary states that adultery is recognized as the only legitimate ground for a permanent
separation, meaning that a spouse who has been cheated on is not required to return to conjugal life (meaning life in common, not just sexual intercourse). The separation may be immediate and without ecclesiastical authority, although a formal separation is to be initiated before the competent ecclesiastical authority within 6 months according to §3. However, because this separation is a right , the ecclesiastical authority cannot refuse the petition, unless the exceptions in §2 (narrowly interpreted) apply. The requirement for petition is so that the judge can attempt to pursuade the innocent spouse to forgive the adulterous spouse and resume common life. The wording in the English translation is the ecclesiastical authority "is to consider carefully whether the innocent spouse can be moved to forgive the fault and not to prolong the separation permanently." This does not mean the judge can order the innocent spouse to forgive and resume conjugal life with the adulterous spouse.
In addition, there is Canon 1153 §1:
If either of the spouses causes grave mental or physical danger to the other spouse or to the offspring or otherwise renders common life too difficult, that spouse gives the other a legitimate cause for leaving, either by decree of the local ordinary or even on his or her own authority if there is danger in delay.
§2: In all cases, when the cause for the separation ceases, conjugal living must be restored unless ecclesiastical authority has established otherwise.
Therefore, spouses can
leave on their own authority before a decree from an ecclesiastical judge is asked for and/or obtained.
The wording on the Phoenix site is not accurate. A divorce decree in the civil forum certainly serves as an indicator that conjugal life
has ended. It does not indicate a marriage, in the sense of the bond, has ceased.
I would bet that most dioceses do not even have a process or a tribunal setup to handle petitions for separation. It's why priests haven't even heard of this. So then what?