Fairly complicated question. I'll start with the basic misconception that the Hodinohso:ni (Iroquois) sided with the British during the American Revolution. [The official policy of the council fire of the 6 nations was neutrality between the British and the French. In 1701 the Hodinohso:ni along with 34 other nations signed the Great Peace of Montreal with France. This was a peace and friendship treaty which ended hostilities in the St.Lawrence watershed and established a trading and protection relationship with France](https://en.wikisource.org/wiki/Translation:Great_Peace_of_Montreal). After the Treaty of Paris the France ceded their interests in Canada. This meant that the Treaty of 1701 was in question. The Annishinabe, for example, rejected British attempts to claim their lands under what was a peace and friendship treaty. This set off Pontiac's war.

The Hodinohso:ni however had pursued their own treaty relationships with England. They extended the covenant chain treaty concept that they had begun with the Dutch to England and saw themselves as brokers of peace between the French and the English. For example early in the revolution the Oneida council sent a message to the governor of New York stating "We are unwilling to join either side of such a contest, for we love you both, Old England and New. Should the Great King of England apply us for aid, we should deny him - and should the colonies apply, we shall refuse. We Indians cannot find or recollect from the traditions of our ancestors any like case." However since the Hodinohso:ni could not coerce it's members to follow it's will there was always a tension between the central council other nations such as the Kanien'kehá:ka (Mohawk) who had their own relationships with their neighbours. One of these neighbours who would have a considerable influence on forging a relationship between English interests and the Kanien'keha:ka was William Johnson.

Johnson had established a reputation as a fair trader with the Kanien'keha:ka and spoke fluent Kanien'keha. As his relationships grew he became the representative of the British government. At the same time he was formally named by the Hodinohso:ni confederacy. Johnson negotiated a number of treaties with the Hodinohso:ni and knew how to conduct diplomacy and the meaning of core treaty concepts such as the great law of peace, the dish with one spoon, and the covenant chain. Johnson was able to use his personal relationships to bring Kanien'keha:ka allies into several conflicts including some of the early battles of the Seven Years War. He was also instrumental in negotiating the Fort Stanwix treaty which was to end western expansion into first nations territory by colonists. Johnson also had a life long relationship with Molly Brant or Degonwadonti, who was clan mother to the wolf clan. In Hodinohso:ni culture the leaders who sit at the council fire are chosen, groomed and removed by the clan mothers. As well Brant's younger sibling Joseph became war chief meaning he represented the interests of the clan mothers and ordinary people at council and held leaders accountable if they strayed from those interests. So Johnson's relationship with Brant meant there were extremely close ties between the council fire of Kanein'keha:ka and England's interests.

Other nations in the Hodinohso:ni were more allied to the Patriot interests. The Oneida were influenced by Samuel Kirkland to join support the newly forming independence movement. The strength of Kanein'keha:ka's relationship with William Johnson and the growing support of the Oneida began to fracture the Hodinohso:ni confederacy. In the winter of 1776 disease ran through the Hodinohso:ni nation and many elders and leaders died. In 1777 the grand council could not come to one mind on the issue of alliances and the central council fire was ritually extinguished leaving each of the Six Nations to pursue their own interests. Some such as the Oneida sided with the Americans. Others such as Onondaga stayed neutral. Kanein'keha:ka, of course, sided with England. After the English defeat the newly formed American government undertook to claim the unceded lands of the Hodinohso:ni the consequences of this are still playing out in American courts.

in addition to the links I also referenced Berleth, Richard "Bloody Mohawk: The French and Indian War & The American Revolution on New York's Frontier" 2009