I am not that experienced in Unreal lighting as you probably are. I’ve worked however, with other rendering engines and I think I know what the solution might be.
Put an additional light (plane light preferably) right behind your window. It must be bluish, very week and as
Problem: There are very few rays from the sky dome coming in through the window. The sky dome has a set number of rays firing and if the opening is small enough you get very few of them actually in the room.
You might be able to increase the number of rays but this would be an “overkill” for your exterior. Also it will increase the baking time tremendously.
You might make the window big enough so enough rays enter the room but that is not always possible especially if you work with real building plans.