the origin of hobbits

[Gwaihir the Windlord]

There may have been some Elven blood in their clan somewhere along the line.

Highly, highly unlikely. Not that I really see anything that Hobbits had in common with the Elves anyway; their society was certainly very much a human one, and down to earth.

As for the Hobbits you mentioned, they did not either. Frodo -- and Bilbo -- were simply different, very intelligent Hobbits that studied Elves, were in contact with them and loved them. In the Took family -- Isengrim etc -- the odd unusual person did crop up, but they were wanderers and travellers rather than Elf-like people, and very much still Hobbits, from what I can gather -- which, as I say above, is a distinctly different state to the Elvish one.