2012 Prius almost shook apart this morning (startup)

I have had my 2010 Prius run very rough, yet not seem to be misfiring. both times was after the car sat for a month or more in winter, seperated by 3 years.
I am not sure my problem is the same one that others complain about. 1 it does not seem to misfire, but yet very rough power pulses,2 the problem does not clear when the engine warms up, 5 + miles driving.
First time it happned, I drove the car several miles and start / stopped the engine several times.

I suspect it is some sort of electronic glitch, as I discovered a "fix" the first time. Remember I had driven the car more than 5 miles and had start / stopped it several times, the engine was fully warm. The "fix" was to step on the brake and shift to N. The engine instantly smoothed out to normal and never happened again for nearly 4 years.
This winter I started the car after a 2 month lay up with a battery maintainer on the 12V battery.
An exact repeat of the original problem, the engine started, seemed to be hitting on all 4, but had a severe vibration. I drove the car until fully warm and start/ stopped it several times, still the severe vibration. I started the engine, running very rough, stepped on the brake and shifted to N, the problem instantly cleared itself and did not return. ????? I suspect an electronic engine control glitch that shifting to N clears, any other theorys ????????

 

In the winter here, even in EV mode, the ICE comes on within a few seconds. I didn't realize, though, that neutral could be used without putting the car in "Ready". Thanks.

 

If you're quick (but careful, of course) you can slip it quickly into R, give it a quick pulse then put it back into N to glide to where you want to park. Push the power button to put it in Park. If you push P the engine will start.
If it's below freezing, I can't do this, because the engine starts within a second or two.

 

True, there are at least several different videos, I even saw one on Camry hybrid.
I actually made one myself after I learned how to reproduce the problem: