The denied boarding compensation (DBC) is paid as soon as the passenger passenger is denied boarding and the alternate transportation is offered. Providing of course that the passenger meets all the check-in requirements. It does not matter if the passenger accepts the alternate transportation or not.
I am going to assume that Reham's wife made the met the carrier's check-in requirements (including being at the gate within x minutes of scheduled departure - too lazy to look up what Delta's is at JFK). Since the alternate arragements is scheduled to arrive more than 4 hours after her original scheduled flight (again, an assumption based on the stated 4 hour layover in France - Paris?), she would be entitled to 200 percent of the fare (for that flight segement, not the entire round trip ticket) for both her AND the child, up to the maximun of $800 per passenger. Just factoring in 1/2 of what you paid: the combined DBC would be $1005 for both your wife and your child. - Please note, that I am just assuming that the one way ticket is 1/2 of what you paid, most likely, it is not.
Since you did not accept the alternate transportation, I would argue that you are entitled to a full refund of the total amount paid. Just like if the flight was cancelled and you did not accept the reaccomodation. Note - the carrier can choose not to refund taxes if they have already paid those taxes to the government(s).
As for why your wife was picked to be denied boarding, Bob is basically right. They did not just pick her. The carriers have a formula for who gets bumped based on a number of variables... Amount paid, check in time, ect. The computers do all the crunching and the agent just reads the name that pops up.
If you want to file a formal complaint with DOT, you can do so at
http://airconsumer.ost.dot.gov/complaints.htm