Almost sounds like bad gas. Is that gasoline more than 1 year old? Also, water in the gas will cause spitting and sputtering. Empty some of that gas into a clear glass jar and let it sit for about an hour to settle then look for a distinct line of separation between the gas and oil.
Any codes set? Any fuel leaks? Also, try loosening the fuel cap enough to relieve the pressure/vacuum and see if that helps. if so replace the fuel cap with the correct type (vented or non-vented).
Well, in that case anything that may cause the current draw to rise may cause the relay failure, whether it be a faulty fuel pump , fuel pump going bad or a short circuit in the wiring. On a 1996 you would need a scan tool to check codes but auto-parts stores usually check them for free.
Has any cleaner been added to the fuel tank, if so it may have knocked loose some dirt, rust, etc from the fuel tank and is now clogging the fuel filter.
Its also possible you may have a few fuel injectors clogging. I hear walmart stores with an auto shop will clean them for $20.
Has the PCM BATT fuse #3 15A ever blown? If so, you may want to check the current draw on the wiring, click here for the wiring diagram.
It would be best to use an inductive (clamp-on) type ammeter. Harbor freight usually sells one for about $20 and sears has some also.
Actually harbor freight has it listed for $12.99.