What is the most durable wood to use for an outdoor swing set
I would highly recommend Cedar.  Similar to Redwood, it is resistant to insects and rot.  If you can source it, Eastern White Cedar is a wonderful wood to make a play set out of, as it wont give splinters as easily as many woods will.

I went a bit overboard on the play set I built last summer.  I went with rough cut western red cedar 4x4s, and jointed/planed them down to about 3 3/4" x 3 3/4".  This allowed me to end up with very square members.  This was necessary as I did everything using mortise and tenon joinery (yes, I went overboard).

The primary problem with cedar warping/twisting is when it is unsupported.  Once supported properly (i.e.- assembled as a structure), the warping/twisting is minimal.