Could be a frozen brake caliper or a rotor that is "out of round".
The car may need a front end aligment. See link below...
when the car isin drive and you take your hands off the steering wheel, for a second or two only (and safety allows it) the car will veer left or right instead of going straight would be good indication that it is misaligned.
Your power steering pump and or steering box may be about to give out on you.
Brake rotors are warped.
The car was then seen to veer off of the road.
have front suspension checked
Sounds like a belt broke in the tire. Need to know what type of SUV.
Can be low tire pressure in left front tire, brake rotor sticking, or front end out of alignment causing it to veer left. Shaking can be bent wheel, defective tire, or brakes grabbing. Have the brakes, tires, and suspension inspected.
If your steering wheel is shaking you probabley messed you wheels or axel up
Turn the steering wheel right to turn right in reverse.
Get the tyres checked for balance, and bulges in the side wall.
i would really like to know myself