In other words, what was the mechanism by which she had such wildly different triplets, assuming the whole controversy is not merely a mistake of translation?

The form seems roughly analogous to Zettai Karen Children and Hanamaru Youchien, except for the trio being siblings now (like Power Puff Girls).

I'd love to say that I'm intrigued by Mitsudomoe, but then I remember well how much Hyakko sucked, and it was billed in a roughly similar way as a slice-of-life show.

FRIDGE: Perhaps it's an artificial insemination procedure gone wrong. I heard they have lots of triplets in China these days. So, just add a little donor mix-up and/or medical malpractice and there you go.