2012 Chevrolet Malibu - Warning lights and shaking

when coming to stop sign stabilitrac and engine light come on and start shaking

What codes are you getting? CEL might trigger the stabilitrac light.

Your ABS is coming on when it should not. Take a mechanic with a scanner for a ride show you can show them the issue and so they can see why the car thinks the ABS should operate. Anything else is a wild guess.

Is that light blinking/flashing?

Just fixed similar problem on Trailblazer. Using scanner, could see one wheel sensor dropping out before the other three. Common problem, sensor output low due to rust under the mounting flange. Removed, cleaned up and working ever since. Check your wheel speeds as you come to stop. You can also check sensor output with DVM on AC volts spinning wheel by hand if you have that option.