No need to remove the ABS module -- just unplug its big electrical connector.We get plenty of bad ABS modules here, and no one has ever reported it shut off their engine. The classic diagnostic for a bad ABS module is the inability to communicate with it, but I'm guessing that's not your problem.
Take the ABS module out entirely and see what happens. While it's out, if the car runs OK send the module to be rebuilt. MUCH cheaper than a new one.
I did have a bad ABS module cause my local smog test station to be unable to scan my car, even though my trusty VCDS OBD-II dongle and software worked fine. I replaced the ABS module with another used one and passed smog easily, but I probably could have passed smog sooner if I had the sense to unplug my ABS module.