My 2008 Equinox does the same exact thing, it seems like the back right tire locks up, and the traction control light comes on. i took it 2 times to the mechanic they have no clue what the problem is. I keep adding break fluid. But they say no leak. It has no pick up and i cant move the car once the break locks up. It seems like the tires are dragging, i smelled the burning rubber.
I am going to try and put my foot under the break . They also made me fix a sensor . I am so fed up with the car at the moment !!!!