there is such helpful function, named selection cycling, it is one of status toggles. You can activate it by combination ctrl+w if I remember well. It allows You to select object hidden behind the other
You can also set up multiple viewports in model space. This allows you to isolate certain views of your drawing or model. The really cool thing about this feature is that you can, for instance, start drawing a line in one viewport, and then extend it directly into the next viewport to connect it to an object in that section of your drawing. This is especially useful for 3D, and is far better than just changing your drawing to a wireframe view; it provides 100% precision. As far as the command I forget, but a simple search of "viewports" in AUTOCAD Help (f1) will definitely show you how. Hope that helps.
I cannot repeat your problem while using wireframe mode. I created a cube. Did a shell of the cube so everything is enclosed like you would have with walls, floor, ceiling. I placed an extruded rectangle on the inside plane, "wall", of the cube. I can select the rectangle with no problems. If the "painting" isn't overlaying other lines, there is no reason you cannot select it due to a "wall" being "in front" of the painting. The only time I have difficulty selecting the rectangle is when I have the Visual Style on a rendered style, such as Conceptual or Shaded. Post your drawing so we can see this problem ourselves. It is hard to diagnose a problem if we can't reproduce it.