Steering wheel shakes when applying brakes while traveling at higher speed, 50mph+. I've already replaced all four tires since they needed to be replaced anyway. Has anyone else had this problem?

Your brakes are warped. Get them machined down and you'll be good to go. You'll likely continue to have this problem every 20K or so until you get new breaks because (I think) the OEM brakes are too light for the size of the vehicle.