Here is the real answer and I learned something. This makes sense.
Smart Native:
Ah, the actual reason why "sa" is used here is because of definitiveness. "Relasyon" here, whether it be "inyong relasyon" or "relasyon mo," is specific; there is a specific relationship being discussed here. As such, when an agent-focused verb is used, it prefers to take "sa.". In the first sentence, the "lamok" that the child killed is just any mosquito; it doesn't pertain to any specific mosquito, so it takes "ng."
My thoughts, this makes sense:
Sino ang pumatáy kay JFK? (JFK is definite)
Sino ang pumatáy ng mga tao? (People is indefinite)
And yeah ni is wrong.