Okay - found out a bit more:
It seems Ruth's father was actually Rabbi Falk Vidaver, not Rabbi Nathan Vidaver, as is often stated. Her grandfather and brother were both named Nathan.
Falk Vidaver was clearly very prominent as a rabbi and writer. He must have been middle-aged when Ruth was born since he was already officiating at marriages as of 1872.
Also, all the ET newspaper blurbs on Ruth put her first husband's name as Fontaine, but I wonder if it was actually Browne. This is given as her previous married name in the 1932 San Francisco Social Register and an alumni note from an SF girls high school with a link below mentions a "Ray [sic?] Vidaver Browne".
A couple notes on Ruth's daughter Vida: she used Dodge as her maiden name (not so uncommon for a stepchild, especially a female stepchild, to do in those days), and she was working on her third husband by the time she was in her early thirties. Married names were Mackay, Thomas and Payne, respectively (actually, perhaps her mother also had three husbands?).
It seems Falk Vidaver's longest affiliations were with synagogues in Boston, San Francisco and New York. The impression I have is taht he only lived in Ohio temporarily, to help establish a synagogue there, and it was during this period that Ruth was born.
I can find out nothing about Ruth's mother, not even a name. A Blue Book and another directory listing Falk in the early 1890's make no mention of a Mrs. Vidaver.
http://www.sfgenealogy.com/sf/schools/ghsjun05.htm
Miss Ray VIDAVER, who married Mr. Thomas BROWN of London...has returned...for a visit...
VARIOUS SOCIAL REGISTER/SOCIAL BLUE BOOK LISTINGS OF THE DODGE/VIDAVER FAMILIES AND THEIR IN-LAWS:
http://www.sfgenealogy.com/sf/1932b/sr32_p.htm
PAYNE, Mr. & Mrs. Arthur C. (Mackay-Thomas-Vida DODGE), 430 E. 86, New York.
http://www.sfgenealogy.com/sf/gnl/srt.htm
Name: Thomas, Mr. and Mrs. John L.
Maiden name: Mackay-Vida Dodge
Clubs:
Phone:
Address:
City:
Remarks: see Dilatory Domiciles
http://freepages.genealogy.rootsweb.com/~npmelton/srp.htm
Name: Payne, Mr. and Mrs. Arthur*and Mr. Clarence
Maiden name: Loree-Elizabeth F. Leary
Clubs:
Phone:
Address:
City:
Remarks: absent
http://www.sfgenealogy.com/sf/1892b/sfb92v.htm
VIDAVER, Rev. Dr. Falk, 916 O'Farrell st.
Link mentioning various marriage performed by Falk Vidaver:
http://www.sfgenealogy.com/sf/vitals/sfmar_a.htm
"ALEXANDER/DAVIS--In this city, March 20, by the Rev. Dr. Falk Vidaver, Isaac ALEXANDER and Lena DAVIS, both of San Francisco." Source: San Francisco Examiner, 22 March 1892, p. 7.
"ALEXANDER/TOBIAS--In this city, May 1, by Rev. Dr. H. Vidaver, J.S. ALEXANDER of Hollister, to Miss Lizzie E. TOBIAS of this city." Source: San Francisco Daily Morning Call, 11 May 1881.
"ASH/RUSSACK--At Reno, Nev., December 7, by the Rev. Dr. Falk Vidaver, Herman ASH and Miss Fannie RUSSACK." Source: San Francisco Examiner, 9 Dec 1890, p.7. Transcribed by Ron Filion.
"COHEN/GOLDSTONE--In this city, March 20, by the Rev. Dr. Falk Vidaver, David COHEN of Boise, Idaho, and Gussie GOLDSTONE of San Francisco." Source: San Francisco Examiner, 22 March 1892, p. 7.
"HISCHFELD/ASHER--In this city, December 14, by the Rev. Dr Falk Vidaver, Marcus HISCHFELD to Miss Minnie ASHER of San Francisco." Source: San Francisco Call, 16 Dec 1884, p. 8. Transcribed by Mary McInnes.
"JACOBS/BOVIE--In Sacramento, June 16, 1891, by the Rev. Dr. Falk Vidaver, Abe JACOBS and Millie BOVIE." Source: San Francisco Morning Call, 18 June 1891.
"VIDAVER/ROSENTHAL--In this city, April 11, by the Rev. Dr. VIDAVER, N.J. VIDAVER and Rosa ROSENTHAL." Source: San Francisco Daily Examiner, 19 April 1888.
http://ajcarchives.org/AJC_DATA/Files/1903_1904_3_SpecialArticles.pdf
Vidaver, Falk. Rabbi and Preacher of Congregation Beth
Israel Bikur Cholim, New York City. Born 1846, in Warsaw,
Poland. Son of Nathan Vidaver. Educated at Warsaw and University
of Berlin (Ph. D.). Rabbinical diploma conferred by the
Rabbinate of Warsaw under Meisels. Held positions in Boston,
Mass.; Evansville, Ind.; San Francisco, Cal.; and Louisville, Ky.
Publications: Notes on the Ethics of the Fathers and on the
Psalms; Articles in the American Israelite, Reform Advocate,
Hamagid, Hazefirah, Hoibri, Hashachar, Hakol, and the Hebrew
press of New York. Address: 181 East 71st, New York City.
http://books.google.com/books?id=weL9M46TcU8C&pg=RA1-PA147&lpg=RA1-PA147&dq=falk+vidaver&source=web&ots=G8M89FIB35&sig=uMDwASiMIdUL0_JcliKPRUYVi-g#PPP 1,M1
[Falk Vidaver replaced brother Henry, who died previous year, as rabbi of SF synagogue]
http://books.google.com/books?id=74WxERjUz0IC&pg=RA1-PA345&lpg=RA1-PA345&dq=falk+vidaver&source=web&ots=VbMR223fx3&sig=2p8VLDLHZwXav31Y1nuKz8jEBGM
[title of book written by Falk Vidaver]
Marriage performed during his Boston days:
http://www.mnopltd.com/jean/her772-1273.html
SEPTEMBER 4, 1873
Ellsworth, 31st ult., at the residence of Lewis Friend, Esq., by the Rev. Falk Vidaver of Boston, assisted by Rev. Dr. Tenney of Ellsworth, Mr. DAVID FRIEND and Miss MATILDA ROTHBART. The marriage was solemnized in accordance with the imposing rites of the Jewish church.
http://books.google.com/books?id=L-kWounhFZcC&pg=RA1-PA351&lpg=RA1-PA351&dq=falk+vidaver&source=web&ots=8hmT9Zfusy&sig=ivkQ93TYjFcW8DjOW63Yi1b7Tnw#PRA 1-PR5,M1
[American Jewish Year Book of 1900-01 with description of Falk’s New York synagogue]
http://www.bij.org/bethisrael.html
[excerpt from 75th birthday of SF’s Beth Israel Temple, which must have been 1935; mentions Falk Vidaver taking part in 1891 dedication ceremonies of newly erected synagogue that was then nearly demolished by ’06 earthquake; not sure Falk was actually connected with SF Beth Israel]
http://www.jewishencyclopedia.com/view.jsp?artid=1362&letter=B
[excerpt on his Boston synagogue]
Early San Francisco Directory:
http://www.damrellsfire.com/cgi-bin/directory_search.pl?ds=7&ln=117857
117895
Vidaver
Falk Rev.
house 19 Pleasant