My maternal side are UEL I have been through the proces it is not difficult although somewhat time consuming if you don't live close to the local chapter (it is a requirement to join). Each has a "genealogist" or researcher that will help assemble the material in the order to which they will accept your application.
That is good to know that they have someone who knows how to look at this information and can piece it together as well as we can, if not better.
In reply to Aghadowey: You are right, I just need proof of the relationship between Jr and Sr. As much as we know it we can't prove it with documentation. How do we know that they are relation beyond Arthur Jr? Letters of little consiquence and oral history. Not enough for the UEL I think.
Census I have seen any of them in show Arthur Jr with his family and Arthur Sr with one his his other children in the same year, and I can't find anything before that. That is the 1871 Census, which shows Silas as Arthur Jr's eldest son as well. Arthur Sr is shown as living with his son Daniel. So a round about way of proving Arthur Jr and Sr are father and son is to show that Arthur and Daniel are brothers. Clunky but it will do the job.
As to where they lived it is hard to tell, I know that Jr was born and raised in Ontario (Belmont was his birth place), he moved back to the USA (I believe in 1887) and died in Detroit in 1904(ish).
Sr is a different story, I do not know if he was born in the US or Canada. My records show Canada (Lennox) but the 1871 census says the USA, so I don't know. And I have no place of death.
Sr married Jane Kelly (1789 – 1881) in 1813
Jr married Clarissa Badgley (1838 – 1918) I believe in the early 1850s (first son was born in 1855)
Hope that helps.