You remembered seeing an ad on television where people would accomplish two things at once by splitting in half vertically. But where that ad was special effects, your new katana could make it a reality.
Rotating the dial until the blade was glowing bright white, you then carefully cut a straight line through the mother from the bottom of her crotch to the top of her head. As you did so, a glowing white line separating her left side from her right side could be seen. Of course, she was still whole, at least for now.
You then went to sit down on a nearby bench to inconspicuously observe them, then pressed the button on the hilt, restarting time. The world got a little fuzzy, but everything cleared up quickly. You noticed some new changes - the mother now had two handbags slumped over her shoulder, and the glow separating the left and right sides of her was gone.
"Enough!" she yelled, getting the attention of both her daughters.
"Since you two won't come to a compromise," she said as she moved one of her handbags to the opposite shoulder, "I'm going to have to split to supervise you with your separate activities."
And with that said, she stepped apart in opposite directions, splitting in two.
"Okay Melissa," said the left half. "I'll take you clothes shopping"
"And Kelly, I'll take you to see the Green Princess", the right half said.
You could see Melissa was rolling her eyes at what her mother had just done. She didn't seem surprised at her mother's ability, just embarrassed. Kelly, however, seemed pleased.
The two halves took their respective daughters and went their separate ways. Their locomotion of the halves was interesting to see too - it almost looked like a mixture of walking on two legs (except one leg was invisible) and hopping.