The way the skylight works you shouldn’t have an issue with your assets under the terrain unless it’s getting light bounces. The biggest thing here is to make sure that if you’re getting light leaking or lighting where you would not want it to have meshes behind your cave mesh to help block this light. You can see that in the Realistic Rendering demo on Marketplace we’ve set that up to help block light as well.
There is no way in UE4 to exclude specific objects from certain lights though. From my understanding this is not possible with deferred lighting.
In the images below These are two setups and they look identical. One with a skylight and dynamic light and the other without a skylight and a dynamic light.
With Skylight in scene
Without Skylight in scene
For the ambient option you can always used a post process in the cave area so that when you enter it will disable the post processing effects you do not wish to have, such as Auto Exposure (aka. Eye adaptation). This will keep your cave nice and dark!
If you have any questions feel free to ask!