Create a new MIDI or Instrument track in PT. At the beginning of the track (or whenever you want to trigger the video) make a new note (have it play for for half a second or so).
Write down what MIDI key goes to what song.
In Resolume, go into Shortcuts and map the video you want to play with the same MIDI note. (Make the shortcut to "this clip")
Rinse and repeat for all your other tracks.
You'll need to setup an internal MIDI loop back.
You'll want PT to output to the Input of this internal loop back, and have Resolume use the internal loop back as it's Input for MIDI.
One I would recommend would be LoopBe Internal MIDI
http://www.nerds.de/en/loopbe1.html
If you're on OSX then you should already have this option built in with the OSX Audio/MIDI feature using an IAC MIDI device.
And again, I can't stress enough how I would not run any other application on the same machine as PT
Unless they made changes in version 12, Having PT run throughout a show without any hangup's or crashes would be a miracle to me.