loose steering and vibration in steering wheel.

I agree with your brother. Your spring bushings may need service but they are not likely causing your steering shimmy. Get the truck into a reputable alignment shop and have a thorough front end inspection completed. Your issue will likely come down to a wheel runout or balance issue or a worn front end component.

 

For the loose steering problem, it can be easy to spot the problem if you open the hood, have it running and just turn the steering wheel shaft by hand back and forth a bit. Keep a close eye on your Pittman arm and drag link, watch every single ball joint for excess play. Everything should be pretty tight. Also grab your steers and try to wiggle them back and forth as if you are trying to turn them left and right. Get someone to help you so you can watch both sides

 

Have you driven the truck since the tires were replaced? Is the shimmy exactly the same, worse or better?
Were the tires balanced on or off the vehicle? I see a lot of mounting issues where the wheels mount to the hub with uni-mount. Look for gaps between the wheels and hubs at the stand offs that could cause an out of round condition. Also sometimes debris can get between the drum and hub or wheel and drum causing issues with runout. You say the steering seems sloppy, where is the slop coming from? A good inspection should find and locate these issues.

 

Parts simply don't go bad instantly once tires are replaced. If you feel the sloppy steering now that it has new tires then therefore the tires are to blame. It is common to have new steers and feel a loose or sloppy feel with new and tall treads on some tires. Your toe set is probably not correct. The shake in the steering wheel is classic steer tires out of round or out of balance. Even if they balanced them, they probably aren't running round and bouncing which could be causing both of your issues. Since you have new steers, it is always a good idea to have the toe set. We always recommend spinning up the tires to make sure they running true and round. 95% of all tire shakes I come across are due to not running round and basically bouncing down the road. That is why balancing over and over never seem to cure the problem. Either the tire is not square to the rim, or the wheel is not perfectly centered on the hub.

 

Possibly toe is set incorrectly, maybe a bit toed out or neutral. Should be toe in 1/16”. Can cause a vibration.

 

Ok, sorry. Best thing to do is see if you have mechanical slop or combination of mechanical and tire flex. With it just sitting and engine off, turn the steering wheel back and forth in the sloppy range before you feel resistance. If you have excessive play in the wheel, like more than a couple of inches, now you need to see where you are losing it at. Could be a sloppy steering column, steering shaft, loose steering gear or draglink-tie rod ends. You generally need two people, one to wiggle and one to watch. If all is tight and this is more of a handling issues, then yes, I highly recommend an alignment.