I just got an RWAP on a book I just got the order 2 days ago, I packaged it up and marked it mailed this morning and I dropped it in the blue bin in town at 3 pm this afternoon! And the requester is being quite rude with me about it and it wasn't even my book! However, it was my book she marked received so I've got that RWAP on my record and she wants ME to be the one to return her credit.

Did you explain the situation to her?  There is an option for her to say it was resolved and then there is an option to choose that she hit it by mistake.  I'd say that's what should happen in this situation.  

The nasty PM and the addition of an incorrect RWAP and a demand that you return her credit for book she has yet to receive, sounds like something TPTB might be willing to step in and assist you with.  This member is being completely unreasonable; why should you return her credit when she hasn't gotten the book you sent?  Sounds like she made a mistake and instead of taking responsibility for marking the wrong book wants you to take the blame.  Good grief!

She's saying now that she wants me to return the credit so that she can give it to the person that she DID get the book from. But if I do that, what's to stop her from refusing to give me my credit when my copy of the book arrives? It's not my fault the original sender (apparently) forgot to mark  the book mailed or otherwise let it time out for some reason so that the request rolled over to me!

Copy the rule in the Help Center about this and send it to her.

She's under no obligation to give a credit to the original sender if her request timed out or if the first sender never marked the book mailed. After the request rolled over to you and you mailed the book, you should receive the credit.

You received the credit when she marked it RWP.  I would contact the team on this one. 

Ugh. Some people just can't control the crazy. If it were me, I'd just shoot her a last email explaining that since she is being a nutball and continuing to make completely stupid demands, that I'm going to contact someone else to clean up her mess for her.

I would tell her that, depending on the circumstances she may not be obligated to give the first person credit, but she is obligated to give you the credit since your's was properly marked mailed so you will not be returning the credit to give to someone else. Since she is the one who made the mistake and gave the credit to you early, she will need to deal with cleaning that up with the other sender on her own but she needs to go into her Transaction Archive and mark that the RWAP was in error. You can direct her to the Help Center - there is a section for marking a book received when it wasn't - suggest contacting a TG in Live Help and have them explain things to her.

I wouldn't worry if she doesn't mark the RWAP as a mistake, the Team can see from the PM exchange that it was the requester's error and they wouldn't hold it against you.

I would contact TPTB on this one and maybe they can clear it up for you .

<<She's under no obligation to give a credit to the original sender if her request timed out or if the first sender never marked the book mailed>>

This isn't quite true.  Only if you end up with 2 copies of the same book and you only requested 1 book.  Then you are not obligated to give to a credit to the first sender who didn't mark the book mailed.  Even if a sender doesn't mark a book mailed, you are obligated to mark the book recieved if you only receive that copy. 

"...Ugh. Some people just can't control the crazy...."  +1

I agree with the above, there's no reason you need to be involved at this point.  You fulfilled the order as requested and your book has not been received yet.  Do not buddy credit(s), you have zero obligation.  If she persists with the cranky, contact TPTB.

The requester should contact her Tour Guide or Live Help, either should be able to assist her with this situation.  There's things she needs to do, but nagging at you isn't one of them.