I was mailed the wrong book, so I PM'ed the sender.  They informed me that they must've mixed up the labels, and sent my book to another member and then sent their book to me. 

I tried to explain to the sender that the best way to straighten it all out, is for them to give me the other person's address, but the sender wants me to mail the book back to them so that they can re-mail the book to the right requester, and that they would repeat the process for the other requester.  I don't want to do that. 

It makes more sense to simply contact the other member so that we can mail these books to each other.  I let the sender know that as long as I end up with the right book then they can have my credit.  Paying to mail the other requester their book in exchange for mine doesn't bother me because this is a $37 book.

I'm pretty sure that English isn't the sender's first language.  I asked them to give me the other member's nickname, so that I can straighten it out with them directly by PM, but the sender said they still hadn't contacted the other person yet, and please send back the book.

What can I do?

I don't think you are really required to return the book to the sender or to the other requester, without reimbursement of the postage.  If the sender offers to pay the postage send it where ever he wants it to go, it shouldn't matter to you as long as you eventually get the book you ordered and are not out any $. If the sender doesn't offer postage, I would mark the book RWAP, and resolve it that way.

From the Help docs:

If you received a book you didn't request (a title you don't recognize), most likely the sender put the wrong book into the PBS wrapper with your address on it. 

If you received the wrong version of a book you requested read There is a problem with a book I received! for instructions.

Well, first of all, if the sender wants you to mail the book back to them, they have to give you a credit to do so (this is in the "help" documents). I agree that the easiest way is to give you the receivers info and have you mail it to them, but again, they need to give you a credit to do so -- it is generous of you to be willing to send it on on your dime, but remember, the other receiver also has to send their book on to you and they also need a credit from the sender to do so. I would refer the sender to the HELP Documents. GOOD LUCK!

I would not mark the book received at all.  You haven't received the book you requested-how can you mark it received even as RWP. 
I would let the original book go lost.  If they give you a credit to cover the postage than I would send them the book back and let them deal with it.  It does make more sense for you to send it to the person who ordered it and vice versa. But it's not worth going back and forth with this person. 

If you want to be generous and send the book back without a credit to cover the postage that's up to you. But I would NOT mark the book you ordered as received RWP.  Then you'll be otu the book you want and the credit you paid for it unless they return it.  And then possibly the postage to send the wrong book back. 

What Mary said.

ditto.

i've actually got mostly the same situation going on too.  sender accidently mailed me book 1 in a series instead of book 2, and must have mailed book 2 to the person who was supposed to get book 1.  she's agreed to give us each a credit as suggested to mail the books to each other, if the other person gets back to her (which last i heard she hadn't).  but as the help documents say, don't mark the book received since you didn't receive it.  the appropriate help topic:  If you receive a book you did not request...

hopefully you'll get it sorted out since it sounds like it might be a harder to get book.  (mine shouldn't be, it's a fairly new mmp release.)

though i was worried about contacting her at first, since i'd just gotten posted another book through FIFO from the same sender.  she did send it - but this time she used PBS-DC instead of mailing through paypal.  :)