Here is some info about the 'relation' between the Von Carlows and the Von Mecklenburg Strelitz:
End of the Mecklenburg-Strelitz line in 1918
(Source: Brückner [president of the Landgrericht in Schwerin]: 'Die mecklenburgische Verfassungsfrage seit 1913,' Jahrbuch des öffentlichen Rechts der Gegenwart (1920), 10:218-225.)
Adolf Friedrich VI, grand-duke of Mecklenburg-Strelitz, committed suicide at Neustrelitz on 23 February 1918. He was the only surviving son of grand-duke Adolf Friedrich V (d. 1914), himself only son of grand-duke Friedrich Wilhelm (d. 1904). The latter's only brother Georg (1824-76) had married a Russian grand-duchess and settled in Russia. He had two sons, Georg (1859-1909) and Karl Michael (1863-1934). Both were general officers in the Russian army. Georg married unequally on Feb 2, 1890, and his only son Georg Alexander (1899-1962) was known as graf von Carlow (title in Mecklenburg conferred on his mother 18 March 1890).
Karl Michael wrote on 24 June 1914 (a few days after the death of Adolf friedrich V) to the new grand-duke Adolf Friedrich VI of Mecklenburg-Strelitz, to inform him of his decision to establish himself permanently in Russia and to renounce any claims he might have as agnate, for himself and any eventual issue from an equal marriage. Adolf Friedrich VI wrote back on 9 July 1914 to give him permission to be naturalized in Russia, but asked him not to make any renunciation at this point. Karl Michael answered back on 16 July an agreed to defer any renunciation until the matter arose.
When Adolf Friedrich VI died, the only agnate left in the Mecklenburg-Strelitz branch was Karl Michael. As Germany was still at war with Russia, and Karl Michael was not only a Russian subject, but also a serving officer in the Russian army, his accession was inconceivable. Jurists consider that the head of the Mecklenburg-Schwerin branch, grand-duke Friedrich Franz IV (1882-1945), could have either exercised a regency in Karl Michael's name, and, should the latter have a son by an equal marriage, until the majority of such son; or he could have excluded Karl Michael by a decision as head of the house. But, since Karl Michael had expressed an intention to renounce his rights when the time came to exercise them, it seemed logical to ask him to confirm that intention. In the meantime, by a decree of 27 February, Friedrich Franz IV took over the administration of the grand-duchy of Mecklenburg-Strelitz. The wartime situation made it difficult to reach Karl Michael; finally, a letter of 17 May reached Karl-Michael on 6 August. He replied by a letter dated 10 August, from Kislowodsk, and unequivocally reaffirmed his renunciation:
"Ich verzichte für mich und meine aus einer ebenbürtigen Ehe möglichen Nachkommen auf alle Thronfolgerechte und die Ausübung der Regentschaft sowohl im Großherzogtum Mecklenburg-Strelitz, als auch überhaupt in den Mecklenburger Landen, und behalte mir, abgesehen von dem Rechte auf die Regierung und die Ausübung einer Regentschaft, alle mir als Agnaten des Strelitzer Hauses zustehenden persönlichen und Vermögensrechte vor, soweit ich darüber nicht mit dem Großherzoge Friedrich Franz etwas anderes vereinbaren sollte."
This letter did not reach Friedrich Franz IV until January 1919 in Denmark.
Two factors complicated the situation. One was the desire on the part of the inhabitants of Strelitz to retain their independence from Schwerin. The other was the will left by Adolf Friedrich VI, dated 29 Sep 1912, in which he bequeathed his whole fortune (amassed by his grandfather Friedrich Wilhelm, and estimated at 30m Marks) to Friedrich Franz of Mecklenburg-Schwerin's second son Christian Ludwig (1912-96), on condition that he become grand-duke of M-Strelitz and take up residence in Neustrelitz; failing that, the inheritance would be reduced to 3m Marks.
In any event, it is doubtful whether Friedrich Franz IV had any possibility of keeping Strelitz separate for his second son, because of the terms of the Hamburg treaty of 8 March 1701 which divided Schwerin and Strelitz; even without such terms, the principle of individual succession by primogeniture had been laid down by the duke Johann Albrecht in his testament of 1573, and later partitions notwithstanding, that principle would have come into play once again.
Nevertheless, Friedrich Franz IV never resolved the matter in time. On November 9, 1918 he dismissed his cabinet and replaced it, promising to introduce a democratic constitution; he also appointed a new cabinet in Strelitz with the understanding that the status of the grand-duchy would be settled by a constitutional assembly. On November 14 he abdicated and left for Denmark on November 16; the cabinet in Strelitz, with the grand-duke's agreement, declared that his regency had also ended.
In 1929, Karl Michael, still unmarried, adopted his nephew Georg Alexander, graf von Carlow. Georg Alexander had two sons by Irena Raievskaia: Georg Alexander (1921-96), who left a son Georg Borwin (b. 1956, with two sons); and Karl Gregor (b. 1933), without issue. The right of this Carlow branch to bear the name "Herzog zu Mecklenburg" was recognized by the hereditary grand-duke and head of house Friedrich Franz on 23 Dec 1949. This branch considers itself to be the remaining line of Mecklenburg-Strelitz.
The senior line of Mecklenburg-Schwerin became extinct in July 2001, with the death of Friedrich Franz IV's eldest son Friedrich Franz. If one considers that the renunciation of Karl Michael in 1918 transferred all the rights to Strelitz to the Schwerin branch, and unless one considers that the Carlow branch has been made dynast since, then the house of Mecklenburg is extinct and the title of grand-duke of Mecklenburg passes to the house of Prussia.