I agree with rainbow that the introductions were done too fast. Perhaps after the kitten is spayed, the lady can start over from step one and this time take several weeks of passing the 2 cat's scent back and forth without them seeing each other. Ensure only positive things are associated with the other cat's smell, like giving high value treats (vanilla ice cream is my cat's ultimate) on top of the other cat's bedding, playing, grooming etc when they swap rooms, stuff like that. Gradually move up to limited viewings (through the crack of a door), and only when there are no reactions to each other, allow them short supervised visits (again with lots of treats and positive rewards). Mucho patience required with this technique, obviously, but there is no better way.
I personally would not use any corrective behaviour in this situation. It can backfire and end up deepening the hostile feelings between the cats because they start to anticipate bad things happening when they're around each other. Simply separate them at the first sign of souring moods (put a pillow between them if there's a risk of getting hurt and "herd" them apart rather than pick one up). Go back a step in the introduction process and try again later.
ETA - I know you know all this 14+, I just think it needs to be reinforced to the lady.
"To close your eyes will not ease another's pain." ~ Chinese Proverb
“We must not refuse to see with our eyes what they must endure with their bodies.” ~ Gretchen Wyler