Some SUV's and 4 x 4s can be rolled by steering wheel turns in excess of 120 degrees. (1/3 turn). Many serious rollover accidents have been caused by incidents of excessive steering. These vehicles should always be driven in a manner that tends to eliminate the possibility of an excessive steering event. The best way to do this is to position both hands on the wheel so that the body blocks the arm swing required to turn the wheel enough to roll the vehicle. You will be much less likely to roll the vehicle if you have a closed grip on the wheel with the hands close together. In emergency situations you may not be inclined to open one hand and release the other to "oversteer". Steering input will probably be restricted to sub-critical levels. At very least, always keep a closed grip on the wheel, so that you would have to release your grip to palm the wheel around. Palming the wheel probably causes a lot of rollovers, learn to avoid doing it.
Parking, low speed turns and other maneuvers will require more steering than that allowed by the correct highway or cruising grip described above. Place plastic tape on the steering wheel to mark the correct hand positions so that you will remember to return to them when driving normally. Each vehicle driver might have their own color tape if you find that there are different hand positions involved for comfortable driving.
2. Returning to the Road.
Extreme caution is required anytime you try to return to the paved surface from an unpaved shoulder or cross a pavement edge. This is true for all vehicles but especially for SUVs and 4 x 4s. A high pavement edge can trip you. And, even if you have only two wheels off the road, a hard turn on the steering wheel - often caused by the resistance generated by wheel contact with the pavement edge - can cause you to roll over. All vehicles have a minimum speed required to roll them. For SUVs and 4 x 4s this is around 30 mph on level ground with normal loads. In theory then, you can't roll the vehicle if your return speed is below 30 mph and you should be safe if you are going slow enough when trying to re-enter the roadway.
The catch is that under certain conditions, and for certain vehicles, minimum rollover speeds can be lower. A Jeep CJ-5 can be rolled at 24 mph and possibly lower speeds. (Big rigs -18 wheelers- can probably be rolled at speeds as low as 5 mph!) Slopes, deflated tires, high, heavy loads and perhaps other conditions can lower these "minimum" speeds, but generally, below 30 mph, you can't roll most light vehicles.
3. Avoidance Maneuvers.
Many SUV and 4 x 4 rollovers are caused by highway avoidance maneuvers- trying to avoid hitting something in the roadway by steering around it. People and vehicles must be avoided of course. But, the cases involving small animals and obstructions are less clear however. Rolling over is so hazardous; 1 rollover in 23 produces a fatality and there are many more serious injuries than deaths; and so easy to do with some vehicles; that trying to steer around most obstacles should be avoided in most SUVs and 4 x 4s. Obstructions that might cause loss of control of the vehicle, by causing tire failure or loss of traction for example, might well be avoided as a general rule especially if steering input is limited by the methods discussed above. But in general, if you don't want to have to run over dogs, cats and other small animals, then don't drive an SUV or 4 x 4. The latest models with computer controlled anti-rollover systems will probably allow you to make emergency avoidance maneuvers without rolling the vehicle, but older models lack this feature. Without this anti-rollover technology, It is probably preferable to have a low speed frontal impact even with larger, heavier obstructions than to try to steer around them. Belted occupants should be safe in frontal impacts at speeds up to at least 35 mph- if you don't have windshield penetration