I had a daughter like that.
When I got divorced ( I got custody )...my eldest daughter decided ( on her own )...(She was 10 years old.)
that SHE was "The Mother" of the household. ( unless I "over-ruled" her ).
I guess it is something "instinctual".
Anyway...it was O.K. ( and a HELP to me....mostly.)
P.S. Fortunately....She got-along well with her older brother who was 12 years old....and VERY independent.
The 2 younger daughters listened to her...mostly.
I think that they still listen to her...though NOT as much. The Youngest one is NOW 38 years old. SHE was also a VERY GOOD Mother to her own children...who are NOW 1 past College (graduated) and 1 entering College. A GOOD MOM.