minimum sampling rate for very short duration signals I understand that sampling rate should be twice the signal bandwidth for successful reconstruction. But what I don't get is how this translates in the time domain.

For example, I have a sine wave pulse with frequency 100MHz and duration of say 50ns. This signal has a bandwidth of 20MHz (1/50ns = 20MHz). Theoretically, I can sample this signal at any frequency above 40Mhz. Let's say I sample at 50MHz, then I only get 2 samples per pulse!! Now what can you possibly do with those 2 samples is my question. In other words, although Nyquist criterion is satisfied in this example, there's not enough data points to proceed.

This kind of signals are common in radar and generally you want to run some sort of matched filtering/correlation once you have digitized the pulse. But you can't run any descent signal processing on just two samples? am I missing something here?
Any signal of finite extent (duration) in one domain (time) has infinite extent (bandwidth) in the other (frequency).  The bandwidth of a short pulse above some noise floor can be extremely high, due to the pulse window's transform convolved with the carrier frequency.  

Sharp edges or cutoffs imply very high bandwidths.  Thus in practice, most designed pulses are shaped closer to Gaussian, with much wider tails than the main pulse lobe (in both domains).

Even so, if you know the exact frequency of an unmodulated fragment of a pure sine wave, then in zero noise, 2 or 3 non-aliased points are theoretically enough to solve the equations for the sinewave's  amplitude and phase.