I'm sorry to hear what your wife has gone through. I would keep it. It's already lost a lot of value; even if you don't disclose the accidents, and even if they don't show up on Carfax, a good dealer will be able to figure it out and give you rock-bottom trade-in.
Under what conditions did these accidents occur?
I'm not saying it's your wife's fault, but I have to remind my wife over and over to turn her lights on when it's rainy weather, even if we can see just fine.
In a black car, it's even more important to BE seen at all
If she keeps her eyes moving watching the roads and scanning the mirrors, she may do better anticipating and avoid being a target=defensive driving. A good driver's class might help.
Where do you find these? It is needed