At the beginning of March, a member made a mistake when sending out books and sent the wrong book to my niece. Because the book was sent to an alternate address, there was no way to mark the book received with a problem. Although the help center says that marking the book "received with a problem" is very important, PBS has made that option impossible in the case of an alternate address.
The other member and I negotiated a solution: my niece was to send the book she got to its intended recipient, and we were to get the book we originally wanted plus two books from her bookshelf for the trouble and expense. I marked the book received so that the request didn't expire and cause another to be ordered, and because marking it received was recommended by a Guide as well as that is my understanding of what is recommended in the Help Center for this situation. My niece sent the book about March 18. The member promised to send the two extra books by March 14.
We have yet to receive any of the promised books and she has quit responding to PMs, although her bookshelf is not on vacation hold.
Any suggestions on what to do?

The non-response to the PM is the part that is so against the rules here. How long has it been since she has answered a PM? More than a week? Are they in a part of the country that has been experiencing bad weather? Snow or tornadoes? I would give it a week from the last PM to them and then if no response send it in to Feedback. Yes they will not be able to intercede, but they should know that the wrong book was sent, an agreement was reached, and the member who made the mistake in the first place has not lived up to their part of the agreement. Poor Niece. I hope she gets her book soon!

If you are sending a polite PM about a problem transaction and someone doesn't respond within a week, you should notify the PBS Admin Team (you can find them in the Help Center.)  Copy and paste the entire PM exchange and include it in your message to them. 

That said, if the member replied, "I mailed them on such-and-such a date" then I would wait 26 days before sending them another PM, since that's the amount of time PBS gives for a book to arrive before being considered lost.

Next time, don't mark the book received until you get the one you ordered--since you didn't actually receive it.  No suggestions that will help you now, though, I'm sorry.  Maybe, possibly she's sent them out by now.