I solved it, in case anyone else has this problem. It is a non-standard mouse thing, which is why it doesn't appear to work at first. Usually in these games, you click on a object then click the pointer of the mouse on where the object should go. NOT in this case. It is irrelevant where your mouse clicks occur, per se
. What matters is the shape of the object itself and making its screen outline match the screen outline of the destination point.
To make the reassembly of the little figure work, click anywhere on an arm or leg, to pick it up, and then notice where the end of the arm/leg is in relation to the joint on the body
where you want to put it. THAT is what matters. Basically, visually line up on screen the two parts of the "joint" and click, regardless of where your mouse might be on the screen. After I figured this out, I was through it all in seconds.