Sometimes cats will react this way because a companion cat has been to the vet and comes back smelling "odd" to them. Sometimes it doesn't bother them, but you never can tell how each cat will react.
Julie's suggestion of wiping a cloth over your 1 year old, and then scent swapping by wiping it over the kitten should prove helpful, and things should settle down once that strangeness has dissipated.
If not, then by all means try the reintroductions again, confining the kitten to one room, and taking things gradually, maybe feeding either side of a closed door to begin with. Hopefully it wont come to that.
It's such a shame she is much younger than they said she was, but it doesnt sound like she's come to any harm from that, and you're doing all the right things for her, so her situation could be a whole lot worse.
When we had Paddy and Flynn and our dog, Tess, trips to the vet used to involve all three of us going in the car, and often Tess's presence seemed to calm them down.