555 timer won't trigger monostable mode unless I add a switch between R12 and ground?
The pulse at the Trigger input is only 100 us.  Does it really need to be so short?  Consider increasing R2, R3, and R4 to 10 K.
There needs to be a pull-down resistor from the base of Q3 to GND.  This assures a complete and rapid turn-off when Q2 turns off.
The circuit will not trigger under any circumstances with the components shown.  Please edit the schematic to show the input signal that is supposed to cause a trigger event.  What are the characteristics of that signal (voltage, frequency, rise time, current drive capability, etc.)?