Q: truck shakes alot at 60 mph & steering wheel has alot of play

Hello - assuming the tire balancing was done correctly, the shaking issues could be either a bent wheel, a separating tire (tread separating from the structural belts) or an out-of-round tire. All of these conditions can be "balanced" but still cause problems like shaking at speed. The tire shop that did your balancing can check for all of these conditions. The loose motion in the steering could be worn tie rods, worn wheel bearings, or a worn steering gearbox. The tire problem will obviously make this worse, and fast. I would suggest a thorough inspection of the front suspension and steering to address all of these issues. A mobile, professional mechanic, such as one from YourMechanic, who will come to your location, diagnose this problem, give you an accurate assessment of damage and cost estimate for repairs