In "The Power of Three", she's leading UNIT with science, but at the moment she's realizing that they're failing, the Doctor says, "Don't despair, Kate. Your dad never did. Kate Stewart, heading up UNIT, changing the way they work. How could you not be? Why did you drop Lethbridge?" He encourages her with the mention of her father, instead of simply pointing out her accomplishments so far.
In "The Day of the Doctor", when she facing down the Zygon, she's doesn't say, "You know I will let this bomb go off because you can see my mind and you know I'll do it." She instead references her father as the source of her steel.
In "Death in Heaven", while there was really nothing she could do to fight off the Master and the Cybermen, again, the Brigadier is brought up for no reason, other than to prepare the audience for the later scene, but again, he pulls attention away from the living characters.
Is there some rule that Kate is not allowed to be a strong character on her own? Must everything she does be weighed in reference to her father? It's ironic that she dropped the "Lethbridge" because she "didn't want any favours," and yet it seems that the scripts are only letting her into the show so that they can bring the Brigadier back in. It's frustrating, because she is one of the very few (the only?) recurring strong female characters in the last four seasons who isn't a femme fatale (except Osgood, who they killed off).