From what we found on the first thread, I'd say that Irene's father was Joseph B Couples, of Madison County, Ohio, married to Mary Ann Charters. Both Irene and her sister Carrie used the name Rice at one time or another. I don't know where that name came from.
1880 with wife (deceased) and 2 daughters in Clark Co. Ohio
occupation: baker
https://www.familysearch.org/ark:/61903/1:1:MZ1J-L7NOne of the replies on that thread mentioned Cincinnati.
Joseph B Couples is in the Cincinnati City Directories from 1882 to 1889 with various occupations. He owned or ran a restaurant, was a solicitor, a baker, and a barber, unless they heard "baker" wrong.
In 1889 the listing included both daughters:
1889 Cincinnati City Directory
Couples Carrie, bookkeeper, home 10 Pleasant
Irene, actress, same address
Joseph B, barber, same address
They aren't in Cincinnati in 1890, but in 1891 to 1894 they are in the NYC City Directories. Maybe later as well, but the collection at ancestry.com isn't too good for 1895 to 1902, which is when I stopped looking.
By 1891 Irene is using the surname Rice:
1891 New York City Directory
Couples, Jos B, baker house 244 W 31st
Rice, Irene actress, house 244 W 31st
In 1892 Irene and her sister Caroline are together at a different address on the same street as their father, and in 1894 there is a listing for them but not their father. All the listings in NYC were as Irene Rice.
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Here is Carrie E Couples using the name Rice as a 2nd given name:
Passport Application for Carrie Rice Couples
born 5 October 1869, Madison County, Ohio
signed 22 October 1895, Kings County, New York
witness: Simon J Lowenthal
https://www.familysearch.org/ark:/61903/1:1:Q24F-FDPNAnd the UK Passenger Arrivals have her arriving Southampton, 8 November 1895 as
Mrs Carrie Rice Couples, 45, wife
with Miss Pearl Rice, 8
The 1880 census said Carrie's middle initial was "E" not "R".