changing watch faces on family members watch

You don't need an iPhone to change the Watch face. Just tap and hold not eh face and swipe to "Add New".

Link to more information: https://support.apple.com/en-us/HT205536

I also have this problem, even when connected to the watch—I can change my daughter’s settings, but the face gallery doesn’t show up as an option. She can’t change it herself because she doesn’t have a phone (which I took to be the whole point of allowing a single phone to manage multiple watches).

At a minimum, load a few watch faces into the watch, and I’d expect the Watch would allow swapping among faces.

If that doesn’t work, log some feedback with Apple. Product Feedback - Apple

Connect the watch to the iPhone and try changing the face again.

I’m not aware of any means to remotely alter the watch face.

They probably have to change it themselves.