Hi Geneva, I found the 1900 and 1910 Censuses and the information "proves" the info in Nannie's obituary. However, I can't find anything on her or A. H. Dinker.
I THINK they married in Walker Creek, Layfayette Co., Arkansas where she was living in 1910. I'd look for her marriage info there which hopefully will provide more info about A. H. You can also post on the Layfayette Co., AR Message Board too.
They must have been living somewhere in 1920 and 1930 and you need to find them in those Censuses to find the daughters first names. Successful Searching!