Hello I have a single PC with All the Divinty series and I was looking to play Divinity Original Sin with my wife. What are the requirements?

1. I have a single copy of the game on one PC. Does one need a second copy of the game to play together on the couch?

2. I can get it to work through the Steam Link and controler just fine. But I cannot get the seond controler to control the second character. Am I missing something? Though this could be related to needing a second copy of the game.

3. Can GOG add another filter to their "Games features" on the store page, say "Co-op within single game copy". Then it is clear if you need to purchase a second copy of the game to play together in Co-op mode or not. Sorry this idea is a little late for the winter sale.

Thanks in advance for all your help.

No, you don't: one PC, one copy of the game.
If you want to play the game in multiplayer mode from two PCs (connected in LAN or online), then you need two copies of the game. You need two controllers in order to play the game in local co-op mode. Steam Link should not prevent you from playing in local co-op mode.
First of all, run the game and create two profiles. Now choose the main profile and start a new game using one controller. Once you reach characters creation screen, press the start button on the second controller and choose the other profile. Now each controller should be controlling one character in the creation screen and in the actual game afterwards. The local co-op feature has been added in the Enhanced Edition of the game and was not available before. Anyway the store page of the game states: «Enhanced Edition features 1000's of enhancements including split-screen cooperative play and Source Hunter DLC.»