Power Steering Pump problems of the 1999 Dodge Durango

Car auto-stopped while conducting driving lesson for my 15-year-old stepdaughter. We were traveling 40mph on a country road at the time. She drifted off the side of the road, said the steering wheel was stuck. I told her to apply the brakes. She said she was and they weren't working either. We went through a stop sign and were very nearly t-boned by cars from both directions. My stepdaughter sensibly did as I instructed and pushed as hard as possible on the brake, managed to stop the car before plunging into the river in front of us. I had been having problems with the car for six months previous to this incident. Two diagnostics reported that the vehicle was auto-stopping but not why this was occurring. A local mechanic suggested it was probably the gas gauge sensor in the fuel pump which made sense to me because everything but the gas gauge worked whenever the car auto-stopped. It would typically restart within 15 minutes or so. I assumed we had solved the problem when the mechanic replaced the fuel pump. I know now that the fuel pump was not the problem although I don't know what is wrong with the car. I have researched this on the internet and found there are hundreds of other people going through the same difficulties with 1999 Dodge Durangos. My wife, stepdaughter and I were very lucky not to have been seriously injured during the driving lesson. This situation needs to be addressed before someone is hurt (if they haven't been already).