You don't understand.As shown below, the output of the differentiator is only -ve going spikes which are already less than Vcc/3. Hence 4Vpp wouldn't be a problem.
Pin 2 is normally at 10V, held there by the 10k resistor in your full schematic (with the 555). Pin 2 must go below 3.33V in order to trigger the 555. 10V-3.33V=6.67V. That is why I said you need a pulse that is at least 7V p-p.