she switched off the engine while in a gas station, with the gear in D.
After driving about 13kms more, the car goes off while in motion and doesn't restart immediately. When it finally does, it shudders until finally stabilising.
I turned off my ignition while in D a few times lately (stoned, old, or both). No problems like you describe.
However, back in 2013 I installed my own Viper alarm system. While doing that, I had the *amazing* idea to put a toggle switch on the gas pump. I could disable my car using a hidden switch. Not the kill switch everyone knows about. It would take a thief months to find mine!
I forgot to turn that on at least 4 times. The experience was exactly what you describe. It would drive about a mile (at most), and then die. When I got it started, it would act very fluttery, stall, no power. It would take 10 miles before it came back. (I think it had something to do with the "brain." I think it makes decisions about how to react to the throttle based upon recent activity, fuel usage, etc. I got the impression it didn't have any lower boundary and "learned" to be starved. It took a few miles to relearn.).
It's a wonder I didn't mess my car up from that.
Anyway, that makes me think you got some bad fuel? Maybe the filter is clogged and you're having a similar behavior as the pump turned off. To me, the part about it taking awhile to get back sounds very familiar.