The reason why the Shuchi and Tuolei clans were very close was because Tuolei's eldest son, Möngke, with the strong support of the second son of Shuchi Batu (the Khan of the Golden Horde), took the position of the Mongol Great Khan from the descendants of Wokoutai and became the Great Khan himself. As a result, Mungo's relationship with Battus was extremely close. During his reign as Great Khan, Möngke basically paid no attention to the Golden Horde in Batu, did not require him to levy taxes, and did not require him to hand over taxes to the national treasury.
However, when Meng Ge died in the Southern Song Dynasty Diaoyu City, the situation changed.

in Mungo
After Möngke's death, Möngke's younger brother Ali Buge ascended to the Khanate throne by the mongol princes and nobles. At that time, Battus had died, and was succeeded by Battus's younger brother Beerge. Brother Ber supported Ali Bugo's ascension to the throne, but he himself did not go, but only sent his two nephews and grandchildren, Kuri Lost and Heshi Cha'er, to participate.
Almost at the same time, Kublai Khan also declared himself the Great Khan at Kaiping in the south of the desert, and he also had the support of the host king Tacha'er (who did not have the support of the northeast king Naiyan, who later rebelled against Kublai Khan), as well as his brother Hulegu and others. And the leader and Ali did not fight.
After four years of war, Kublai Khan defeated Ali Bu Brother and became the Great Khan.
Although Kublai Khan won the battle, he did not have the support of the other three khanates (the Golden Horde, the Chagatai Khanate, and the Wokoutai Khanate).
First, the Khan of the Golden Horde, Belgo, did not recognize Kublai Khan's status.
(Kublai Khan called Khan)
Originally, during the Möngke period, the Golden Horde was almost independent. At this time, Bergo also maintained his independent status as always, and did not send emissaries to congratulate Kublai Khan.
At the same time, Brother Ber and Hulagu, who supported Kublai Khan, were openly at odds. The reason is that Hulagu, during the Third Western Expedition, slaughtered The Muslims and executed the Caliph without authorization. Bergo, on the other hand, converted to Islam. Therefore, belgoti soldiers fought a great battle with Hulagu.
Kublai Khan knew of this, so Becky did not issue a declaration of support for him, and he did not pay any attention to it.
The leader of the Chagatai Khanate, Ulugh Kuna, and Mulasa did not support Kublai Khan, nor did the grandsons of Wokoutai support Kublai Khan.
Kublai Khan was waiting for an opportunity.
He first intervened by force, supporting Chagatai's grandson Ba la to seize the Khan's throne. In this way, the Chagatai Khanate was subordinated to Kublai Khan.com.
However, at this time, a grandson of Wokoutai, Haidu, suddenly broke Kublai Khan's plan.
(Haidu)
After Möngke seized the Khanate of wokoutai's descendants, he sent these grandsons of wokoutai to various places for surveillance. However, after Möngke's death, Haidu took advantage of kublai khan and Ali's brotherly killing each other, as well as Kublai Khan's attack on the Southern Song Dynasty, and suddenly rose up to unite the grandsons of Wokoutai and join forces with Timur to attack Bala.
Timur was the son of Battus, and by this time Brother Ber had died, and Timur had succeeded to the Khan's throne. Haidu came to unite with him, and he naturally agreed for his own benefit. Thus, the Golden Horde, though not nominally opposed to Kublai Khan, made actual moves against it.
Haidu, supported by timur the busy brother, was defeated and later died. The khans of the Chagatai Khanate were arbitrarily deposed by Haidu.
At this time, Kublai Khan sent his son Namkhan with Möngke's son Siriji and others to attack Haidu. As a result, Sarigi rebelled, kidnapped Namukhan, and handed him over to Timur, a busy brother.
Timur needed to make a choice at this time. If he had detained Kublai Khan's son all the time, he would have openly made enemies of Kublai Khan.
When Namukhan was captured, Kublai Khan hurriedly sent his most capable general Boyan back from the southern Song Dynasty battlefield to attack Haidu. Haidu could not win the battle and fled west.
Therefore, Timur made the right choice, handed over Namukhan to Kublai Khan, and recognized Kublai Khan's status.
Since then, the descendants of the Shuchi clan have officially recognized Kublai Khan's status as the suzerainty of the Yuan Dynasty, but still retained their independence and autonomy.
(References: "History of the Yuan", "Secret History of Mongolia")