THE TOOLS OF THE TRADE
Though the beauty and power of its swing recommend it, the wrecking ball is not precise enough to remove your now separated section. It does, however, have an equivalent among hand tools that will serve this purpose admirably. It is called a sledge hammer. The sledge hammer's primary purpose is to knock things down, a stubborn stud for example or a recalcitrant window frame.
Be careful about the application of its force as a sledge hammer can certainly pack a punch. It is especially important to keep this tool out of the hands of novices, such as your wife, who have no previous experience with destruction.
When my wife got hold of the sledge hammer, she found her capacity to manipulate objects had increased geometrically. She got carried away when I wasn't looking and laid waste to a side of the garage that I had not intended to lose. I had to forcibly take the instrument out of her hands before she knocked the foundation out from under the house. They say power corrupts; believe it. Under normal circumstances, she is a level headed woman.
For those who can maintain self-control, the sledge hammer becomes a finely-tuned instrument. It can be favorably compared to a bowling ball. Both the ball and the sledge are used to knock things down. They come in various weights, which are custom fitted to the user and to the job at hand. In some cases they can be used interchangeably. I have found the twelve-pound sledge to be ideal for picking up spares. (The best technique is a curving toss with some spin on the handle.)
Probably your most useful tool with regard to destruction is the crowbar. Besides being handy for breaking and entering (if you are inclined toward this activity), it serves as an all around disassembly device. In demolition, you will primarily be prying. That is, pulling drywall from boards, siding from 2X4s and studs from top plates. Be sure to buy a heavy duty crowbar as some of the pry bars on the market do not stand up to the rigors of the job. It is not a pleasant experience to have a bar break in the middle of a particularly strong tug. It is likely to turn you into a figurative sledge, with your forehead putting a hole in the drywall. Depending on the relative make-up of your skull, this may or may not be a painful occurrence.