Yes, indeed! I wonder if it was that Mollie married this T.A. Hamer (what sort of confidence that this is Frank?), and that the Hamer family stories has it that she drowned rather than admitting to a divorce?
I didn't put it in my earlier post, but without something else, seeing "Widowed" in the census doesn't give me surety that the spouse is dead! Much too easy to give that response rather than explain the real circumstances back then, I guess.
So does this fit so far?
Mollie marries "T".A. Hamer 19 Mar 1911 in Waller Co - Frank Hamer had been City Marshall in Navasota since 1908. And around the time of the marriage, he started working as a special investigator in Houston.
And it would have been about 1916 that Frank Hamer met his next to be wife: Gladys Johnson Sims.
So sometime between 1911 and 1916 they divorced?