I can confirm that Turner keeps surfacing. But for me, I also kept getting Drake as a surname for Nancy. I have some records my late great-aunt put together that say Turner as her surname...I can track them down for you in about a week. Currently I'm moving.
I don't think the Drake would work as well, however, because Jesse (note: his name is more commonly spelled this way or Jessee) had a son, Thomas A. Lester, who married Margaret Peggy Drake. I think someone simply got confused and thought that Margaret was Nancy's daughter from another marraige. Totally wrong.
Sorry I can't find anything any farther back for Nancy, but I've traced Jesse back like you wouldn't believe.
To Francis Lester, b. 1591.
Ancestry totally blows my mind.
Please e-mail me if you think I can be of any help to you.