Q: Minivan sways and brakes fade out

I was driving on a 6% downgrade on a highway and applied the brakes three times for about 3-5 seconds each time. This occurred within a 5-minute space of time. The third time I did it the brakes began to badly cavitate. The minivan swayed and the brakes faded out. For several days, the brakes started making a rubbing sound. Also, there is a grinding noise and feel when I apply the brakes when turning. I took the minivan to a dealership and was told that they could not find anything wrong with the brakes. They continued that this type of thing was common for brakes to fade going downhill. They suggested that I downshift to compensate. They could not tell me why the brakes sound like they are grinding when I am turning and they told me that the brakes were fine. I am thinking that the problem might be that the brake rotors are too small for the size of the minivan. They might be heating up too fast and then fade out, plus the rotors begin to warp. I think this could be corrected with enlarging the rotor size and also the brake shoe size since the wheel well has plenty of room in it. Do you agree that this would correct the problem?