Bill and Sam kidnapped "Red Chief" so they could get the two thousand dollars they needed to pull off another scheme in Illinois. The boy is so rambunctious and annoying that Bill can barely stand it. In fact, at one point, Bill actually tries to return the boy while Sam is sending out the ransom note. But the boy returns. It becomes clear to Bill and Sam that the boy is unbearable. This is a satire of how energetic young children can be. It is an example of hyperbole (exaggeration) that the boy would be so annoying that his captors would be willing to give up the plan to get a ransom and would rather just get rid of the kid.
The bottom line is that Bill just couldn't handle looking after the kid anymore.
I tell you, Sam, a human can only stand so much. I takes him by the neck of his clothes and drags him down the mountain. On the way he kicks my legs black-and-blue from the knees down; and I've got to have two or three bites on my thumb and hand cauterized.
In the end, they are not surprised that Mr. Dorset turns the tables and asks them for money. Again, this is satire, but remember that Bill tried and could not get rid of Red Chief. So, they agree to pay Mr. Dorset: a comedic reversal of the concept of a ransom/kidnapping scheme.