Isaac Cole (1772-1842) is my 3rd great grandfather. I note that most family trees on Ancestry have made an error with respect to Isaac's parents and family.
There were indeed two Isaac Cole's who are cousins that came to Canada about the same time as United Empire Loyalists.
My direct line Isaac Cole was the son of Simon Isaac Cole (1735-1797) and Maria Trombauer (1745-1839). This Isaac was born in Rhinebeck, New York and married Hannah Davenport (1785-1817). They had three children, namely Petrus (Peter), Christina and Isaac.
My Cousin Isaac Cole (1774-1825) was the son of Daniel Cole (1731-1836) and Maria Delong. He was born in Pouchkeepsie, New York.
I hope that this will help you correct your tree. You are welcome to review my tree named Cole Family Tree. All of these Cole's were United Empire Loyalists. As far as I know the two branches of the Cole family knew each other and my Isaac had difficulty obtaining his land grant because the government thought that he had already obtained land. So, documents had to be filed to distinquish between the two men.
Both Daniel Cole and Simon Isaac Cole had acted as spies for the British. They both lost considerable amounts of land because of their allegience to Britain and were forced to petition for land from the Canadian government when they arrived in Canada.
I am proud to have both of these branches of the Cole family to be related to me. Please feel free to contact me if you ha ve any questions or comments.