Ideally, your tank should be cycling to 0 ammonia and nitrites within 24 hours before you add animals. The bacteria that turn ammonia into nitrites colonize and multiply much faster than the bacteria that turn nitrites into nitrates. Nitrite spikes can kill fish just as easily as ammonia spikes. It took me 5 months with a raw 20 gallon for it to cycle. Took 1 1/2 months with a seeded 10 gallon, using media from my established tank. In both, the ammonia levels were fine waaaay before the nitrite levels were safe.
I, personally, have never cycled with fish in the tank. I think it's cruel.
If your ammonia, nitrite and nitrates are all good and fish are still dying, you need to get your water tested more seriously. Specifically kH, gH and heavy metals. You can use bottled RO water if your tap isn't safe, but this gets expensive.
Also; is it possible that the 4-year-old is contaminating the tank...? My little sister had a betta fish and the tank went all cloudy and the poor thing went belly-up. Took 10 years for her to admit that she poured milk in there.
It's also worth examining what you're putting in that tank. I've never used fake plants or decor and don't trust most of them. I've also thoroughly rinsed and treated all wood, rock or substrate I've put in my tanks.
Some woods release toxins that will kill fish and some rocks can dramatically alter your water chemistry.
