If someone works full-time at one facility and part-time somewhere else, but the employer needs them more at the second site, can the employer ‘choose’ for them to go to the second site?

The short answer is yes.  When setting out your preferences, they will be considered by the employer, but the will ultimately decide where the staffing need is greatest.  The tricky part of your question is how does the employer ensure that you are made ‘whole’ in this instance; they have committed to that in the cohorting principles document.  And that part is still being determined.