Sam,
You had the car hooked up to a scanner, found a code for a bad wheel sensor and replaced it. All good.
You still have a problem - not so good.
Scan it again, maybe you have a different sensor also failing, or the same sensor code again because of a defective new part or maybe it was the wire to the sensor, not the sensor itself. Everytine you turn the steering wheel left and right the sensor wire to the front wheels bends to accomodate that turn. You have been bending it back and forth for ten years now. Or as you suggest an abs module problem if it cannot read a sensor properly.
Scan for codes, diagnose the circuit (don't just change the part) make the repair.

(I know the ABS and TCS are linked, just not sure how)
More than simply linked it is the same system.
The ABS module and sensors measure wheel speed and have control over the brake system. For the most part they should all be pretty close within the differences of the turning radius from left side to right side as you go around a corner.
When the ABS module detects your foot on the brake pedal and a wheel gets slower than the other three it recognizes that it is skidding and blocks fluid to the brake at that wheel to get it rolling equally with the others and you do not skid, lose traction and control of your car while braking.
When the ABS module detects your foot on the gas pedal and it sees one wheel get faster than the other three it recognizes that it has lost traction is not gripping the road. It has broken loose from the road and is slipping. Using the exact same parts the ABS computer applies braking to the slipping wheel and power shifts to the wheel still holding the road and the car gets traction and gets moving again.
It is not really that simple as the module calculates for engine rpm vs transmission rpm, which gear you are in, how fast you are moving, has the torque converter engaged and more, but basically what I described above is what goes on.

Hope that helps,
Steven