Hi,
I'm don't have much experience with hubs later than 1970 but, sounds like what we'd call coaster brake 'snap' if the hub was an old New Departure Model D. The snap happens as soon as you stop pedaling and like you say, something is binding or catching. On the old 30s-60s model D's it's usually one of the stack of disks a bit bent and catches in the keyway. I've cleaned and overhauled a couple of more modern hubs that are probably from the 80s or 90s and the only part I can think of that might do that is if there is a spring that could be bent just enough that it catches or maybe a brake shoe with a high spot? Take a look at a schematic for the model and do a search for trouble shooting references. Someone out there must have had the same problem and started a thread on some forum. Good luck with it.
Gary