I was going to say I never had any major E-Stop issues with my Denford Cyclone lathe (from what I've seen, Denford used a pretty standard E-stop setup across most of their machines), but then the KFlop allowed me a lot more flexibility in handling E-stops, and I added extra relays so the servo fault outputs triggered an E-stop. However to achieve clearing a drive fault situation, I had to use a custom program in the KFlop that clears the E-stop signal, then waits for all the drives to exit fault status before resuming normal business.
I used Kinco servos from Zapp, which allowed me to configure inputs/outputs how I wanted them to work, but I'm not sure what drives you're using, or what timing sequence they need.
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I'm guessing your problem is the Drive Enable/Drive Fault timing once you're into an e-stop?
Your DER should be connected to a Drive Enable output from Mach3, so unless Mach is active, nothing should move. Simplest option may be to add an override push button to disconnect the drive fault input and/or trigger the drive reset so you can fool Mach into exiting an e-stop, and get the drives back online/out of fault.