Hello I am reviewing the wiring diagram and had a flashback about a problem car I had. Have you replaced the hydraulic pump for the ABS unit.
From what I can see the valve relay feeds the hydaulic valve unit. This is then an input to the control module. I chased this for a while and have done everything you have. Check wiring, swap control module, everything looked good. I had to contact BMW engineering and they had me replace the hydaulic unit as the module is checking the resistence throught the valve block of the hydraulic unit and if it sees an incorrect resistence it sets a fault.
You should have power from fuse 55 for the relay to pin 8 at the relay. The switching side of the relay is the module itself. It then should provide power to the pump. Pin 37(module) to pin 4(relay) is the activation side of relay.Pin 2(relay) to pin 15 of the (Hydraulic unit) is supply for the unit to the internal valves. If there is a problem in the internal valves this could show up as this fault.
Check the wiring for continuity and also short to ground. That is with both connectors unplugged and using dvom on on pin and other to ground you should see an open and no continuity. One thing I like to do in the shop when all else fails is to cut the wire and run my own external wire from connector to connector. This will prove out all the wiring and all it takes is a simple solder and heat shrink to close them back up.
I hope this helps!!!!
BMW Mechanic
Level 1 BMW Master Certification, 9 Years Dealer experience, Team Leader, Shop Foreman