Faces in Photos not correctly synchronized across Macs

I have a collection of about 20,000 photos that I imported from iPhoto to Photos on my Mac Desktop computer. It correctly imported all the Faces. However, when I then shared my Photos library via iCloud to my laptop (opening Photos for the first time on my laptop, and telling it to use iCloud), the Faces were only kind of transferred. That is to say, if I search for the Faces, then it finds them. However, if when looked in the Faces album, it had no Faces in there, and suggested I start adding faces. I did that, but it doesn't merge the previously annotated faces with the newly annotated ones. Indeed, if I look at a photo that has faces that I annotated previously, telling it to show Face names, it shows no faces or face names. Yet, if I search for the people in that photo that I annotated previously, then it finds the photo. My conclusion is that the Faces feature, and specifically the sharing of Faces with iCloud is completely broken, and not written with people who want their photo libraries duplicated across multiple computers (for safety's sake, as well as I just happen to have more than one computer). If anyone has any insight into how to make this work correctly, I'd appreciate knowing it!