While i think it may be odd for Eugenie to be moving to KP; I think this is part of larger plan to free up some SJP space for business offices during a long overdue BP renovation. They had to wait til after HM 90th birthday celebrations and after summer to minimize the losses of tourist revenue. It makes sense to me that over the next few months, the business offices at BP will be relocating to St James and to Windsor.
I can see why Eugenie might want to move to Ivy Cottage, she might like her own place.
But as for freeing up space in SJP, what about Beatrice? Won't she still need that apartment that she shared with Eugenie?