Car wants to die after switching gear

The car is a 2000 Toyota Corolla.

Recently within the past 2 weeks, a strange phenomenon was observed. I would start the car. If I back out of a parking spot in R gear with my foot on the break pedal, then switch to the D gear, as soon as I take my foot off the break pedal, the engine makes a strange turbulent trembling noise, followed by weakened engine sound. Sometimes it dies at this time, but most of the time it "lives through" this weakened state. Does this sound like a transmission problem, or what? Thank you for any advice you can give .
Just as a test in a safe spot, try putting the car in R then hold it there with just the parking brake. From there do the same move but use the parking brake and get into D and see if it still does that. Please do this away from hazzards as a test. I think your power brake booster is replenishing it's vacuum too fast or just plain leaks and goes unnoticed when regular brakes are not in use.

That could just be a check valve and not too hard to fix. It's not so old I would suspect the vacuum booster but who knows?

T
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Tom Greenleaf - MetroWest, Boston
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