I suspect that you may be getting noise and trash from the VFD and spindle into your 120 Volt electrical source, and it is present in the voltage going to the computer and other electronics. It can cause weird problems.
Get an EMI/ RFI filter and install it in the 120 VAC power source to the spindle.
Also, a simple test is to get the 120 VAC power for the computer and drives from a different branch circuit or different location. A better test would be to get the VFD and spindle power from your neighbor or a portable generator for determining whether the VFD is the cause. A Portable generator would be the best test.
Get a portable AM radio, tune it to a weak or medium AM signal, and place it near the machine. See if the radio gets a lot of static or noise when the spindle is turned on and running. Tune the radio thru the entire AM band a few times and see if it is stronger at some locations. If so, EMI /RFI is most likely your problem.
Hope this helps.