"The party wrote me a note and said that this is not to be reported as income that its an exchange."

Who is "the party" ?  Some people here have clients and others have customers, but I'm not familiar with that term.  If someone is telling you how to prepare the return, best course of action is to tell them to prepare it themselves.  

Time shares are more or less in the same category as used cars.  It's surprising when one has increased in value.  And dealers manipulate the prices so what may have happened here is that a couple of "properties" worth $100K were traded for another worth $150K, with another $90K thrown in because, well, parties are stupid. The numbers on paper are just to help fool the next party.  

I have a client who is a retired salesman and enjoys negotiating just for the fun of it.  He owns a timeshare in Mexico but negotiated for the purchase of another (with no intention of actually concluding the sale).  The price started at $30,000 and he got it down to $11,500.  That's the kind of people you are dealing with here.