Until you get it fixed, pull the smaller ABS fuse. It will stop the ABS from kicking in.
I have been chasing this problem. Took readings on my front sensors and they were fine, but messed one up taking the reading and cleaning it, and the problem got real bad. Replaced it and it was better but still there. Replaced the other side, no change. Replaced the back sensor, no change.
I now think I needs new rotors, pads, and to rebuild my calipers so everything it top quality on both sides. Hopefully that will fix it. In the meantime, I just drive with the fuse out.
I am old school anyway and know to pump the breaks in ice and snow.