The other thing to consider is that swapping between two obviously different cars might not be helping at this stage. A bit of continuity might be what's needed. Seasoned drivers thing nothing of jumping from one car to another but that's because the process of actually driving the car takes so little of our cognitive resources that we have plenty to throw at coping with an unfamiliar gearchange, for example. It's not the same during the early stages of learning.
Another option might be to see if her instructor would be prepared to take her out in her car for a session.
I really think, if she's making progress with an instructor in his car, it's too early to write off the tigra as a bad idea. Maybe park it up for a couple of weeks, let her progress without worrying about switching between two cars, and start afresh when she's progressed a little further. It'll come with time, and once it's the only car she drives she'll get used to it.
Also beware that, as you have said, the instructor is teaching different methods to the ones you employ. The fact is there's no right way to drive a car, but it's important that she's taught consistently between you and the instructor so I would not go against what he's teaching her.
Kevin