How are conflicting views concerning latae sententiae excommunications resolved in the Catholic Church? One might identify the real-world problem behind this question. I have
  tried to put it forth without naming anyone involved in such situation
  and instead posed it as an imaginary situation. Please answer in a
  general way and not by pointing at any specific instance, person or
  group.


Imagine the following situation in the Catholic Church: Some catholic commits an offense which is punishable with a latae sententiae exommunication according to canon law.

As I understand the offender will (at least if the offense is somehow public) be advised by some authority (e.g. the pope or the local bishop) that his actions are leading him into excommunication and that he should stop it.

Now let's further imagine that the offender himself argues that his actions were out of grave necessity. In this case he would not be excommunicated latae sententiae (again, according to my understanding of the matter). He thus continues committing the same offense out of perceived necessity.

On the other hand, the relevant authority (pope/bishop) does not accept his arguments and continues to put forth that the offender is excommunicated as long as the offense continues.

This might now lead to a "but he said"-situation where one group claims that the person in question is and the other group that he is not excommunicated, thus leading to major problems concerning the unity of the church.

My Question: In such a situation, what mechanism is there to create clarity about the status (excommunicated or not) of the offender for himself and the public?
This is a basic case of basic canon law. There is no room for 'my opinion' or 'their opinion.'

Canon 1323.
The following are not subject to a penalty when they have violated a law or precept:
1° a person who has not yet completed the sixteenth year of age;
2° a person who without negligence was ignorant that he or she violated a law or precept; inadvertence and error are equivalent to ignorance;
3° a person who acted due to physical force or a chance occurrence which the person could not foresee or, if foreseen, avoid;
4° a person who acted coerced by grave fear, even if only relatively grave, or due to necessity or grave inconvenience unless the act is intrinsically evil or tends to the harm of souls;
5° a person who acted with due moderation against an unjust aggressor for the sake of legitimate self defense or defense of another;
6° a person who lacked the use of reason, without prejudice to the prescripts of cann. 1324, §1, n. 2 and 1325;
7° a person who without negligence thought that one of the circumstances mentioned in nn. 4 or 5 was present.
Canon 1324.
§1 The perpretrator of a violation is not exempted from penalty, but the penalty prescribed in the law or precept must be diminished, or a penance substituted in its place, if the offence was committed by:
1° one who had only an imperfect use of reason;
2° one who was lacking the use of reason because of culpable drunkenness or other mental disturbance of a similar kind;
3° one who acted in the heat of passion which, while serious, nevertheless did not precede or hinder all mental deliberation and consent of the will, provided that the passion itself had not been deliberately stimulated or nourished
4° a minor who has completed the sixteenth year of age;
5° one who was compelled by grave fear, even if only relative, or by reason of necessity or grave inconvenience, if the act is intrinsically evil or tends to be harmful to souls;
6° one who acted in lawful self-defence or defence of another against an unjust aggressor, but did not observe due moderation;
7° one who acted against another person who was gravely and unjustly provocative;
8° one who erroneously, but culpably, thought that some one of the circumstances existed which are mentioned in Can. 1323, nn. 4 or 5;
9° one who through no personal fault was unaware that a penalty was attached to the law or precept;
10° one who acted without full imputability, provided it remained grave.
§2 A judge can do the same if there is any other circumstance present which would reduce the gravity of the offence.
§3 In the circumstances mentioned in §1, the offender is not bound by a latae sententiae penalty.

You said,

On the other hand, the relevant authority (pope/bishop) does not accept his arguments and continues to put forth that the offender is excommunicated as long as the offense continues.

The pope may be the supreme judge (i.e. as to having final say, not as to be being the best or most prudent judge of matters), but he is a judge nonetheless: since latae sententiae is defined in canon law, commenting or declaring anything concerning that penalty stands or falls on whether it is what canon law prescribes, since &quot;x falls under latae sententiae&quot; is an assertion—the pope can't make something true by simply asserting it. If the pope says, 'the book of Genesis says in verse 78 of chapter 90...' there doesn't suddenly become a 90th chapter of Genesis because the pope asserted there is a 90th chapter of Genesis. Likewise, he cannot say 'x falls under latae sententiae' if he in fact does not according to canon law. Moreover, such a mistaken assertion does not automatically convert into a directly imposed excommunication (ferendae sententiae).
What you describe is simply a pope who is not going by canon law, which protects the assumed innocence principle when considering their subjective experience/declared motives (Can. 1234.8). To ignore a declared subjective motive is to ignore canon law 1234.

In such a situation, what mechanism is there to create clarity about the status (excommunicated or not) of the offender for himself and the public?

There is no other recourse (apart from making an argument from reason, perhaps) apart from simply pointing to established law.