Placebo is very powerful and is actually validated by scientific research.

So when the conditions are here, as they seemingly were for your daughters, it's great.

Yet, homeopathy, when considered as a potent product, didn't help, because it is not potent. The conditions enabling the placebo effect did. And no one would complain about that :)

The problem arises when homeopathy is sold and marketed as potent _per se_.