Hi Lisa, Thank you for your interest.
To answer your question as best as I can, Julia is on the 1860 census as Julia Whitney, age 22 and I think she is still on the 1865 State census, although it only gives ages of people, but then she disappears after that. Also, it doesn't give relationship on the 1860 census. Jane however, age 6 in 1860 stays with James Whitney and is in later censuses, referred to as his daughter. Her name seems to become Elida, so I am wondering if she was originally Eliza Jane and the Eliza has become Elida.
Elida Whitney married Elias Wren on 20th May 1888. I have found her down as Lida Wren, on the 1900 census for Chariton, Lucas County, Iowa and it gives her birthdate as June 1853. I have, courtesy of a gentleman who is in charge of the 'Find a Grave' for Chariton, got Elida's death certificate, and on it, it states father - unknown. I have also found her on the 1910 census and it says that she came to the U.S. in 1856, although in her obituary, it says that she was only 2 years old when she came to America, so I suppose it could have been 1855. Elida passed away in 1914.
I am thinking that Julia and Jane could have possibly been a relative of James and perhaps not called Whitney. If they were mother and daughter, Julia would have been very young when she had Jane, also very young to travel on their own. Perhaps Julia's parents sent her away because she had had an illigitimate child. There are so many different possibilities here, that it will be a miracle if we get to the bottom of it!
Best wishes Diana