Hadn't thought about this question in a while. I think the answer would be something like this. Technically, "Niño" and "Niña" mean child and "Hija" means daughter. In common English, swapping out "daughter" for "child" in this sentence would be common and the meaning wouldn't change (and the same would likely be true in Spanish) but even in English, daughter and child are different words. If they were just seeing if you understand the meaning of the sentence I think "You cannot control your child" would be correct, but technically speaking, it does change the meaning of one of the words, and DL is testing your knowledge of words as well as comprehension.
You cannot control his daughter = (Tú) no puedes controlar a su hija
I suppose you're confused about the conjugations of tú and usted (which is the same as él and ella's)
You cannot control his daughter = (Usted) no puede controlar a su hija
You cannot control your daughter = (Usted) no puede controlar a su hija
It's ambiguous, but just in sentences like these (without context). In a real conversation or in a longer text you'll know if it's using 3rd singular person (él, ella) or which treatment form is using with you (tú, usted or even vos).
Pueden is for Ellos, ellas and ustedes for example: Ellos no pueden controlar a su hija...
su could be your (using usted or ustedes), his, her and their.... yes, it's ambiguous.
Sorry, I'm a spanish speaker, I didn't understand so well what you meant... I hope I had clarified your doubt.
EDIT: I'm gonna write the conjugation of poder (can)
Tú puedes, Vos podés