Dude, sounds like your heart is in the right place, but bribery is a bad idea. Turning it into an outright competition between them all was an even worse idea. She needs to be self-motivated to stick with it. Training with her friends makes sense because it’s a community and they can share the experience. It’s a big part of why CrossFit, Curves, and Weight Watchers are popular.
Give this a read for how to adjust your approach in general:
As for getting the pull-ups, neutral-grip is the strongest pulling position, so use that the majority of the time, if not exclusively. Negatives are fine, but they can bring more soreness than standard tempo training, which can be a buzzkill. Band assisted is a better way to go because it lets you get reps in while working the full ROM.
I also like working a lot of horizontal rows (do not tell her they’re sometimes called fat man rows) because you can adjust the angle up or down from set to set based on performance.
This article also has some cues and tips for getting to a pull-up: