My Santa Fe makes the steering wheel shake when braking only does it after going over 40 mph and braking
WAG, warped brake rotors.
^ Probably this. How many miles are on your current brakes and what are your driving habits? Hard stops can cause the rotors to warp.
It could also cause tires that are out of balance.
Unlikely. If it was the tire, that shake would happen whether the brake was applied or not.