My ABS and traction lights are on and car rides.

If that beak is on the part of the wire between the sensor and the connector, there really isn't a good way to fix that other than by replacing the sensor. They have to remain flexible. Any type of splicing method will leave it with a stiff spot and the wires will break right next to that splice. Be aware too that GM likes to use expensive assemblies rather than many smaller parts because it makes putting the car together on the assembly line faster. On a lot of models you have to buy the entire wheel bearing assembly to get the wheel speed sensor. Some of those have a very short wire on the sensor, then the longer flexible one plugs into that. If that extension cable is what has the break, you may get away with replacing just that, but it will likely have to be purchased through the dealer.

For sure the lights will be on. The Anti-Lock Computer will detect the break in the wires right away and turn the yellow ABS warning light on before the car starts moving. That's the clue it's an electrical problem and not something mechanical. The traction control is an add-on system to the ABS, and it can't work when it doesn't know how fast all four wheels are turning, so that shuts down too and the light comes on to tell you.

Neither of those systems should contribute to any ride-quality issues. There's way too many things to consider when you say "bumpy". Your best bet is to have a mechanic take it on a test drive with you. Suspension and alignment specialists will know exactly where to start looking based on their observations more so than from a description of the problem.