Do you have information to support that the Hattie Carr who died in 1920 is yours? I've seen birth dates that were off on gravestones, but that seems really far off.
It might help to look at any marriage or death records for your grandfather and his siblings, so you can see who are listed as their parents. Since the 1910 census says Joseph was on his 2nd marriage, I agree that they may have a different mother than Hattie.
