When I push softly on the brake to slow down, the steering wheel shakes. It does not do it of I push hard or stop quickly.
shaky steering wheel on 1997 Volvo 960
Looks like the brake rotors are warped. Get them checked and resurfaced or replaced them if necessary.
Your rotors have brake material built on them which causes the caliper to pulse and that makes your steering wheel shake. Your Volvo's rotor are not serviceable meaning they can't be machined but can easily be replaced. Your brake job is only $400ish.
THIS IS A SIGN THAT YOUR FRONT BRAKE ROTORS ARE WARPED, MUCH LIKE Zee Tech, YOU SHOULD GET THEM REPLACED OR MACHINED. i HOPE THIS HELPS.TAKE CARE.