Atmega MCU freezes when nearby VSD starts. Possible causes and solutions
You are injecting charges into the substrate, into paths that generate pulses upsetting the internal state of the MCU.
Since even the &quot;RESET&quot; button fails, there is an internal LATCHUP event; this probably draws locally high current, acting like a 4-layer (SCR) diode and only releasing its (undesired) state when you cycle the power to ZERO.
SUMMARY: use TwistedPairs for your Sensing.
I'd suspect massive transients on the sensing_lines to the VSD current monitor connections.
You should have Clamp Diodes on those lines (both of the lines) to prevent voltage excursion beyond the MCU rails. Use low-voltage-turnon Schottky diodes.
To ease the energy-absorption task for the new diodes, install 1,000 ohm resistors in (both) sense lines, in series between the new diodes and the VSD.
Ohhhhh You are using a Ground plane, right? Otherwise the effective Loop Area for magnetic flux aggressors will be 100X larger area than if you had a plane.
For fast switching of the currents, on order of 50 nanoseconds, the Ground (or power) planes begin to have useful (10+dB) attenuation.
For slow switching of the currents, 1,000 nanoseconds or 1uS, the planes will have little or no effect on the magnetic field (which is really just displacement currents induced by changing electric fields).
As other answers suggest, have 0.1uF bypass caps directly at the MCU, between all VDD/GND pairs.
How bad can this get? Here is some (magnetic field) math:

Vinduce = [(MUo * MUr * LoopArea)/(2 * PI * Distance_Loop_to_Wire)] * dI/dT

which simplifies to (using MUo = 4 * pi * 1e-7, MUr = 1 for air, copper, FR4)

Vinduce = (2e-7 * Area/Distance) * dI/dT

and these variables

10cm distance between the high_current spikes in the VSD, and your PCB

LoopArea of 10cm by 10cm on your PCB

dI/dT in your VSD of 100 amps in 100 nanoSeconds


The induced voltage into your PCB, or into Sense Lines, is

Vinduce = 2e-7 * (10cm * 10cm)/10cm * 100 amps/100nanoSeconds

or

Vinduce = 1e-7 * 1e-2 * 1e+9 = 2 volts, which can be of EITHER polarity.

So yes, this hypothesized event and variables is a viable cause.
Ahhhh the LoopArea could be the Sense+/Sense- wires, or the Sense/Return wires.
To minimize the Loop Area, and indeed have some useful cancellation of Vinduce, use a TWISTED PAIR for those 2 wires.