Re: Caine / Kane
Hi Nina, your biggest problem is going to be finding your family's home location in Ireland. John Kane was born 1859, so before civil registration of births commenced in 1864. But your family may well appear in Griffith's Primary Valuations ca 1850s, if you knew which county and parish to search. A Y-DNA test (a simple cheel swab of one of your male Kane relations) is likely to identify which of the several O'Cathain (mow Cain, Kane etc) you family belong to, which will point to one of the traditional clan territories in Ireland.
Kane is considered by most people to be an Ulster name, & so it is often, but there were also separate O'Cathain clans or septs in Co Galway, Co Clare & elsewhere. But a Y-DNA test will tell.