Advice needed: good ways to implement networking into turn-based card game

I am creating a two player card game in Unity. Ideally, I would this: for each player to see his own hand face-up, to see the other player's hand face-down, opposite from them, and to see the cards "in play," on the table, as facing right-side-up.

In other words, something like this:

(One difference is that, in my game, the cards are not symmetric and thus would look different from different perspectives.)
The issue: if I make the cards in each player's hand network-aware, how do I then ensure that the two players sees a different table (i.e. Player 1 sees his hand face up at the bottom of his screen, and Player 2 sees his hand face up at the bottom of his screen)?
Potential (makeshift) solution: I thought, perhaps, I could write a script to disable Player 1's hand on Player 2's screen, and vice versa, or something to that effect. This would require the script to be able to uniquely identify each client running the script. I think this might be possible, and that this solution would work. But to make it work fully - so that Player 1 sees Player 2's hand face-down, at the top of the screen, instead of not at all - would require changing the position of Player 2's hand on Player 1's screen (and vice versa) at every single update cycle of the game.

It's a sloppy solution. Could anyone recommend to me a better course of action? I'm new to Unity and to Unity Networking, but I've read all of the documentation on Networking and couldn't find anything useful. I've also extensively searched the forums with little success.

Thank you in advance for your time.