Abs light comes when I accelarate to make a right or left turn from a side street or if I accelerate hard from a dead stop

Two things can make the bat light come on at idle but go off above idle.
The belt could be slipping because it is not tight, or glazed, or the alternator could be defective.
Once the engine starts, the alternator should be making enough current to "turn the light off". The light is grounded thru the alternator until it is charging, which reverses that circuit and kills the ground source for the light.
If you are sure the belt is ok, I would have the alternator bench tested, because usually if the belt is slipping it slips more at higher speeds.

check for central position of the rack/ steering box. If there has been recent work on the steering ,it is possible that the box/rack was not in the straight ahead position before it was connected up.

Vehicle Dynamic Control, measures inputs from different sensors ie: wheel speed from ABS wheel sensors, trans gear position & speed, Yaw rate, throttle position, etc then makes determination on how to best control veh in a certain situation (accelerating to hard through a turn, wheel spin on wet pavement, sliding during hard stops and such). Can do one or a combination of commands to recover an out of control veh like release brake psi to locked wheel (ABS), limit accelerator, down shift trans, even transfer shift power from side to side/frt to back on some models.

I doubt either problem would cause the issue. The sensor would turn the abs light on, but that disables the abs brakes. The axle either works or it doesn't.

Most likely you have a defective ABS sensor which is part off the front bearing assembly. you will need have or if you have a code reader capable of reading abs codes find the wheel that is causing the code. Then source the part and if you have the ability to replace it replace it. The code/ light should go out when the abs signal is getting correct information.

sounds like a pad wear worning

gmc envoy i had done the same wound up replacing all four wheel brake pads and light stayed off

May have a problem with the hub assembly. some manufacturers combine the sensor and hub into one unit. check those
4X4: may be CV shaft issue. hard to say without hearing and inspecting the pickup.

Your brakes will still work fine. All the ABS does is keep your tires from locking up during very hard stop. What you have is a bad wheel speed sensor located on both the left or right front hub. cant tell which side but a scanner may tell which one is bad. dont worry brakes will work just fine and stop normally. have a good day !!

Check the emergency brake pedal and the brake pedal, just to be sure.