Have the rear disc brakes inspected for rusty/pitted rotors. If the vehicle has an automatic transmission you probably never use the parking brake. Use of the parking brake is what keeps the rear brakes properly adjusted. If the rear brakes are out of adjustment the brakes pads don’t come in contact the rear brake rotors under normal braking. This results in the rear rotors rusting/pitting. Then when the brakes are applied heavily, the rear brake pads come in contact with the rusted/pitted rotors and the rear brakes grab unevenly causing the rear of the vehicle to be unstable.
Here’s what the rear rotors looked like on the wife’s 97 Accord when she complained of the same problem. She now uses the parking brake to keep the rear brakes properly adjusted.
Tester