The fact that Q3 connecting GND to A-GND doesn't really make sense in the first place and your explanation of why its there is not helpful into understanding its purpose. Are you trying to say Q3 is supposed to be a low-side load-switch? Because saying it connects two grounds together means something else and is nonsensical.
If what I assumed about it being a low-side load switch is correct, then your your description of a Vcc dip means that a large current startup current is being drawn by the oscillator circuit. There's too much inductance and not enough decoupling capacitors nearby so it the current surge produces a voltage sag which is browning out your microcontroller. This is made worse by the lower resistance of the AO3400. Increasing the gate resistor should help since it slows down the time it takes for Q3 to turn on and spread the current surge out over time, spreading the voltage sag out over a longer period of time thereby reducing its peak, but what you should really do place another 1uF to 10uF decoupling cap close and in parallel close to the oscillator circuit and its low-side switch.
You also have no high frequency decoupling caps anywhere on any of your ICs. All you have is C5 as a 10uF bulk decoupling capacitor and that is not enough. Your MCU could have possibly not resetted if you had such a cap on the MCU. Put a 0.1uF ceramic cap in parallel with EVERY pair of power pins on EVERY IC, and as close as possible to such pins.