I have just installed a Doug Thorley Header with new cat. and muffler with 2" tubing all the way back. When I run my 1989 Suzuki Sidekick from start to about 45 mph jumping on the throttle it has back pressure and sputters. I also installed a used AC system in it and had to replace the single pulley coming off the crank to a double pulley to accept the AC. I'm trying to give as much info as you might need to give me some ideas.

. When I run my 1989 Suzuki Sidekick from start to about 45 mph jumping on the throttle it has back pressure and sputters. 

  How do you know it is a back pressure problem? Have you measured the back pressure?

Have you driven it very far? The ECU will need time to adapt to the new fuelling requirements. Did you use a new O2 sensor? If you haven't disconnected the battery then I would do that first. That will set the fuelling back to base settings then it will adjust from there.
Also make sure you have no exhaust leaks, that all the vacuum pipes are in good condition and that the timing and valve lash are set properly.
Unless you have a bad cat then it won't be a back pressure problem. It could be that the new pipe just exaggerates a problem that was already there.