What are the current views of the Catholic Church on the right to secession?

In the fascinating article "Catholic Sources and the Declaration of Independence," Rev. John C. Rager, S.T.D., lists some parallels between the U.S.'s Declaration of Independence and St. Robert Bellarmine's and St. Thomas Aquinas's thought. Regarding "The right to change the government," he writes:

Declaration of Independence: “Whenever any form of government becomes destructive of these ends, it is the right of the people to alter or abolish it, and to institute a new government...Prudence, indeed, will dictate that governments long established should not be changed for light and transient reasons.”

Bellarmine: “For legitimate reasons the people can change the government to an aristocracy or a democracy or vice versa” (“De Laicis,” c. 6). “The people never transfers its powers to a king so completely but that it reserves to itself the right of receiving back this power” (Recognitio de Laicis, c. 6).

St Thomas: “If any society of people have a right of choosing a king, then the king so established can be deposed by them without injustice, or his power can be curbed, when by tyranny he abuses his regal power” (“De Rege et Regno,” Bk. I, c. 6).

The morality of secession is related to the tyrannicide (killing of tyrants) thesis of the Spanish scholastic Jesuit Fr. Juan de Mariana, ch. 5 of his De Rege.

The economist Jesús Huerta de Soto, who specializes in Spanish scholasticism, describes Fr. De Mariana's thesis in his article "Juan de Mariana and the Spanish Scholastics" (cf. his related lecture):

Although Father Juan de Mariana wrote many books, the first one with a libertarian content was, perhaps, the book entitled De rege et regis institutione (“On the King and the Royal Institution”) published in 1598, in which he set forth his famous defence of tyrannicide. According to Mariana any individual citizen can justly assassinate a king who imposes taxes without the people’s consent, seizes the property of individuals and squanders it, or prevents a meeting of a democratic parliament.⁷ The doctrines contained in this book were apparently used to justify the assassination of the French tyrant kings Henry III and Henry IV and the book was burned in Paris by the executioner as a result of a decree issued by the Parliament of Paris on July 4, 1610.⁸

In Spain, although the authorities were not enthusiastic about it, the book was respected. In fact, all Mariana did was to take the idea that natural law is morally superior to the might of the state to its logical conclusion. This idea had previously been developed in detail by the great founder of international law, the Dominican Francisco de Vitoria (1485-1546), who began the Spanish scholastic tradition of denouncing the conquest and particularly the enslavement of the Indians by the Spaniards in the New World.

^{Notes
⁷Mariana describes the tyrant as follows:}

^{He seizes the property of individuals and squanders it, impelled as he is by the unkingly vices of lust, avarice, cruelty, and fraud … Tyrants, indeed, try to injure and ruin everybody, but they direct their attack especially against rich and upright men throughout the realm. They consider the good more suspect than the evil; and the virtue which they themselves lack is most formidable to them … They expel the better men from the commonwealth on the principle that whatever is exalted in the kingdom should be laid low … They exhaust all the rest so that they can not unite by demanding new tributes from them daily, by stirring up quarrels among the citizens, and by joining war to war. They build huge works at the expense and the suffering of the citizens. Whence the pyramids of Egypt were born … The tyrant necessarily fears that those whom he terrorizes and holds as slaves will attempt to overthrow him … Thus he forbids the citizens to congregate together, to meet in assemblies, and to discuss the commonwealth altogether, taking from them by secret-police methods the opportunity of free speaking and freely listening so that they are not even allowed to complain freely.
—Murray N. Rothbard, Economic Thought before Adam Smith, op. cit., pp. 118-119.}

^{⁸See Juan de Mariana, Discurso de las enfermedades de la Compañía, imprenta de Don Gabriel Ramírez, calle de Barrionuevo, Madrid, año de 1768, “Dissertation on the author, and the legitimacy of this discourse”, p. 53.}

An interesting part of Prof. Huerta de Soto's lecture (@17:54):

But Mariana insists on another very important idea. He says natural law is vastly superior to the power of each king or ruler. This is an essential idea that is still perfectly applicable today. I believe that we must be aware of and very proud of the fact that when Thomas Jefferson, the founding father of the United States, was considering whether or not to rise up against the king of England, in order to give encouragement to Madison and the rest of the founding fathers of the great American homeland, he says to them: "You only have to read one book: The History of Spain by Fr. Juan de Mariana." And, in fact, Madison even sent him a copy of the book [vol. 2; here's a scan of Madison's copy on Internet Archive], because it is a history of Spain written from the perspective of freedom, unmasking the tyrants.

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It indeed is Catholic teaching that natural law is superior to human law. For the relationship between Divine, natural, and human law, see St. Thomas Aquinas's Treatise on Law (Summa Theologica I-II qq. 90-108).

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Also, see the article "The Shipwreck of Secession" by Catholic author John Horvat II