nate, its been awhile since i have worked on one of them but i will blow out some cob webs and see what we can figure out.
first off i need a little refresher.a 1988 3.8l that carburated correct or is it thottle body injection or multi-port?
if its carburated then i would say the stalling at abrupt stops is more than likely a failed dashpot(its in a vacuum line)
there is a DATA link diagnostic connector under the dash,take a paper clip,straighten it ou then form a "u" with it.there will be two terminals in the diagnostic connector
that are side by side,when you place the paper clip in them with the key on (if your in the correct ones) it will cause the "check engine" light to start flashing
it will flash once then pause then flash twic then pause a little longer and then flash once them twice again(these are numeric codes) it will flash the code "12" 3 times(this is normal and shows its in diag mode)after the last of the code 12 flashes if there are codes in the system it will flahs them out in the same manner,count them and write them down.it will flash each one 3 times(i believe) then go on to the next code.once they have all flashed it will do code 12 3 times again.let us know what codes there are.
as far as the rattle at idle Patb is right on the money there.that is the first thing i would check is for loose heat shields.
what happens when an exhuast heat shiled gets loose it becomes quite sensitive to "harmonic vibrations".these harmonic vibrations change with engine rpm.
when you bring the car off idle the harmonics change and the vibration stops.hose clamps work quit well on exhaust heats shieilds
if it was a vacuum leak it woiuld be more consistant and would run poorly at idle especially on a cold engine.as far as a plugged cat convertor,more than likely not.if that were the case after the engine warmed up you would loose power and would barely be able to accelerate.its possible an egr vlave,but im gonna say at this time doubtfull.these older ones when they fail they usually fail completly and if ythat were the case.lets say it fails in the stuck open position,then it would die at idle al the time as egr gases would be flowing constantly and at idle that will cause the engine to stall.if it fails closed then you would end up with poor accel at cruising speeds and other problems that you havent described.
as far as blowing into or sucking on the vacuum line goes,well it takes approx 17"-21" of mercury to pull enough vacuum to pull that diaphragm.if you got that kind o fpower i wan meet your sister
,beside you realy dont want to be sucking on a rubber vacuum line that has had years worth of carbon and petroleum vapors goinf thru it.not just unhealthy but it leaves some serious black marks on your lips to boot.
let me know whats what. o.k.
we will get this figured out for ya
peace,
tim