LJ has some interesting info but what I don't like about the idea is that if the wall, or walls, that you insulate have a stairway, or anything where adding 'layers' will reduce space, it's likely to look a bit odd. In other words, if you have a stairway that's right up against the wall, and it's carpeted, LJ's suggestion might reduce the width of the stairway by an inch or more. If this is the case, will you re-do the carpeting on the steps so it looks 'right'. Also, that inch can be critical when it comes to moving furniture. You may or may not be able to more or remove something to or from the 2nd floor.
Obviously, the best way to solve this problem is to open the walls up and soundproof. Maybe you only have to do the living room wall(s). (The dining room may be quiet; your call.) OR, you can sell and more to a place that has cement block between the units. This will DEFINITELY give you some quiet. Besides, in some municipalities, cement block is required by code as a fire prevention barrier. How 'bout where you live? You can all your local county/town/township and find out what the minimum code requirement for adjoining walls is in your municipality. If you do sell and/or move, DO get proof of what's between the walls. Hopefully, it's block.
My best to ya and hope this helps.
PS: I use to move furniture for a store and I can tell you for a fact that furniture mfgrs. do design some of the products in such a way that they consider a 30" doorway or hallway or opening. It's a marketing thing to be able to get the 'biggest thing' into the house while still considering that it has to get from the front door to its destination.