Me and my friend are trying to connect to each other using hamachi. We can see each other in the game list, but when we try to connect to one another the game just hangs on the please wait screen for about a minute then it just goes back to the normal multiplayer screen with no error

GameRanger will probably suit your needs a lot better than Hamachi when it comes to DK2 (or any other game from GOG) given that it has built-in support for a large range of old and new games. You can get it here.