If Kaoru was Takeru's elder sister, then what we know of Kotoha's family inheritance means she is probably "entitled" to Shinken Red, but they both have the power.
It's also possible that Kaoru is the only Shiba by blood and Takeru was adopted so the family would have a male decoy to draw away the Gedoushuu's attention.
To this day it's not too uncommon for a more traditional Japanese family that only has female children to adopt a boy just so there's a male heir, or so I've read.