Do the same for the mods as you did for the map.
Once you have the mod files in your dominions3 mod folder, start the game and enable the mod in preferences. When you create a new game, the mod will automagically be enabled whenever you play that game in the future, even if you disabled it for another game.
For example, if you were playing 2 games and game1 was created with mod1 enabled and game2 was created with mod2 enabled, you would not need to mess with the mod preferences again. When you play game1 you would only see the changes caused by mod1. Mod2 would only be seen when you played game2.
(Glad that worked for you!
)