Boy, your relatives really wanted to make it tough to find them, didn't they? Do you know why they were living apart like that?
Do you have a date or even month of death for Jeremiah, along with a town on Long Island? I would recommend contacting the public library in the town he died in and getting an obituary. That should list kids (it is very possible there were more kids born after 1930), married names, and maybe even grandkids. Usually if you email with the relevant information and ask them the procedure, they will send it along. Worse case scenario is that it will cost a minimal amount.
Kath