I think Debie's census listings should answer some of your questions.

It looks like I missed Ralph Dixon/Dickson in both 1920 and 1930, my apologies for that!

This Ralph is (as you said) the son of Harry and Annie Dixon in 1900, who are living next door to Clay and Sarah Dixon that I mentioned in my previous reply. Since Sarah seems to have had a lot of children, I would guess that Harry is the son of Clay and Sarah.

When you said that Rose had a younger brother Ralph, How do you know that? Do you have a document of some kind or is it what you were told? If it's hearsay, then could it be that Ralph was of a different relationship (maybe cousin/nephew), not a brother?

To me that family of Clay and Sarah Dixon would be my first priority, that either Fannie or Matilda could be Rose in 1900. You need to find marriages for Fannie or Matilda Dixon/Dickson, just so you can rule them out as being Rose. If the person who told you about Ralph is still alive (I'm assuming it is hearsay), Can you also ask that person if any other names in the 1900 household is familiar?

Clay
Sarah
Matilda
Fannie and
Willie

And also if any name in Harry's 1900 household (where Ralph was to be born) is familiar?

Harry
Annie
Willie and
Pearly C (or Corine in 1910)

The Amos I found in 1870 is living by himself as a domestic servant (born 1859). The Izora I found was actually not Izora, it was Isadora, living in the household of George and Lydia Dixon in 1870 (7 years old).

Thanks,
Johan