My guess is that the more experience you've got with
foreground/background reversion images and random-dot stereograms, the
easier it is for you to make her change direction. I don't have much
trouble -- but I did computer vision research early in my career.

I used to know a guy (decades ago) who'd been one of the microcode
authors of an early computer graphics display that did hardware 3D
transformations. In testing the unit, they spent a lot of time doing
cross-eyed stereo imaging. He told me when he went to get his
driver's licence renewed and they gave him some of the
eye-coordination tests (for instance, a bunch of circles visible from
your left eye and a vertical line visible from your right: what
circle do you see the line going through?) they concluded he had no
eye coordination at all....