I am NOT a mechanic whatsoever. But the problem does not sound like a tranny problem to me at all. As was pointed out, I think the car idles rough and stalls because of a maintenance backlog.If filter are clogged and spark plugs get old, I believe a rough idle is very common. And, of course, revving it up will prevent it from doing so. That you have to put it in neutral to rev it up is most likely only a coincidence. It would also not stall if you revved it up in drive and went - you’d just run the red light 
I had a similar problem recently and it turned out to be a cracked plastic boot in the air intake. The car wouldn’t get enough air and stall.
Take it with a grain of salt as I am not a mechanic but if I read that spark plugs have last been changed 120K miles ago I suspect some sort of maintenance backlog. Remedies were profoundly laid out by cigroller above.