Rewire is some kind of audio interface for software. All applications supporting it can "talk" to each other.
For example: Cubase & Reason support Rewire so I can use Cubase a my sequencer and use the Reason sounds. All audio is digitally routed into Cubase and it's in perfect synchro.
Recycle is a audio tool that can "chop" loops and samples (eg. drumloops) into smaller samples to be used in your sequencer.
For example: you have a drumloop that goes "boom-tsjak-boom-tsjaka-tsjak". Recycle will chop this up into different pieces: "boom", "tsjak", "boom", "tsjaka" and "tsjak". with these bits of sound you can changes your beats, create fills, ... "tsjak-boom-tsjaka-boom-tsjak".
Recycle is a stand-alone tool.
I don't know if DP supports the Rewire protocol. If it does: load up DP, load up Reason, activate Rewire inputs and off you go.
If it doesn't, things get complicated. You could try sync'ing 2 computers via MIDI or in the case of having only one computer using a MIDI routing tool (eg. Hubi's LoopBack Tool).
I use Reason every day and love it. The strings they have sound amazing from their site.
Herwig