Unfortunately I never figured out how to get two computers to communicate. For two player all you can do is take turns.
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I made that for the Dominion game but you technically have to share a mouse pointer. Since you don't have to do anything during your opponent's turn in Pokemon having only one screen should work aside from being able to see your opponent's hand. I may eventually add a feature to hide the cards in your hand between turns.
Not sure I want to put 30000+ lines of code online. But I'll give you some advice. I have all the cards defined in text files which the program parses to understand each card effect step by step (I basically created a unique scripting language for card effects). As for online I used an asset package called Mirror in my Weiss Schwarz simulator and got it working on LAN. Unity is supposed to be coming out with a new multiplayer system, but I haven't heard much about it.