From what I've been able to find Col. Timothy S Williams (Alice's maternal uncle) died in 1930. Several years before Alice disappeared. Perhaps portions of her inheritance were depended on her reaching a certain age or properties being sold, etc...?
I was under the impression that upon Col. Williams' death his assets were bequeathed to his wife and when she died the assets were then distributed to Alice and any other heirs. (Just my assumption based on other info previously posted... I could be wrong).
http://fultonhistory.com/Newspaper4...y News 1942 Jul-May 1944 Grayscale - 0035.pdf