The first think you need to find out is if it is the engine or the trans. Just because you had the trans done doesn't mean that is the problem. A lot of what you have said leads me to think it is the engine that is stalling and it is what is making the shuttering.

where did the transmission come from? junkyard, transmission shop. or auto parts store ( won't name the supplier that does most auto part store transmissions) but they have a 65% come back rate. find local shop at ATRA.COM did you replace the transmission because of this problem. then might not be the transmission at all

There appears to be a HUGE supply of poor quality amateur rebuilt transmissions out there. You get what you pay for. I'd suggest finding a better quality transmission shop that guarantees their work.

very confusing matter do a search with the search engines it could actually help

Replaced trans with supposed rebuilt unit (47re).Worked great for 4 days then started to shutter when slowing/stopping and now it will work fine on start up but after 2-3 minutes of running the truck if you shift into reverse the truck will buck and it stalls the engine.Will also stall when you shift into drive too but the truck has to run a little longer before it will do it in forward gears.Installed a new torque converter and lock-up solenoid and still doing the same,any suggestions?Thnx for your answers,time and help.