If I hit a bump in the road the rear end jumps to the right

Is this a rear end problem or could you have a front end going too?
The correct tires are, also, important.

Replace rear shock absorbers.
Their function is to maintain contact between tires and floor. When they are worn the wheels spend too much time in the air without any traction.

sounds like you got a inner tie rod end that is bad

Not sure from that description but i would check for a broken belt on the tire. If not check tir rod.

bad suspension in the rear

Bad shocks will cause the front jump around. Also check the tires for uneven wear.
The entire front end should be looked over if the shocks are bad you may also have other parts worn as well.

The bumps do initiate the shaking. When my 2006 Ram 2500 4x4 started shaking, I had just had it aligned that morning. A month or so before that alignment, my passenger side outer tie-rod broke while driving down a rock road. I replaced it with a heavy duty MOOG tie-rod end. Anyway, the same day I had it aligned I was driving back home from a job and towing my bobcat behind me. I hit a bump and the truck did the "death wobble" with the front end shaking violently up and down in an alternating fashion (one tire in the air while one tire on the ground and then vice-versa). I changed the tires first (which were worn-out 305/75/17 mud tires). Since the day I bought the truck new in Jan. 2006, I've had larger tires on the truck than the tiny 235/75/17s that came with it and I've done a lot of heavy towing with it and never had a problem until this alignment was done at Sears. I;m still trying to figure out if it was the alignment specs that they used or if the problem coincidentally started that same day. I also changed the steering stabilizer. Neither the new tires nor the stabilizer/damper helped the problem. So I changed the other outer tie-rod end and the upper and lower ball joints (all MOOG with grease fittings). I turns out they were worn out. So, the truck no longer shakes violently up and down when I hit a bump. That problem seems to be in check. However, now when I hit a bump the truck's front end wobbles side-to-side. I can do a few things to recover from it. I can hit the brakes pretty hard and sudden (which can cause an accident on the interstate), or I can **** the steering wheel side-to-side a few times (from 10 o'clock to 2 o'clock) and that stops it immediately...until the next bump in the road. Also, if I let my foot off the accelerator just before hitting a bump and let the truck coast over it instead of power through it, sometimes the truck will ride over the bump without incident. I found out yesterday on a 5 1/2 hour road trip that if I did 80 to 90 miles per hour and powered through every road blemish, the truck rode fine...no shaking at all. I suppose the high speed forces the tires to stay straight when they hit a bump. Lastly, to confuse my problem solving attempts further, sometimes the truck rides like a cadillac (for an hour or so) at regular speeds and no matter what bumps I hit. Then without worning, the front end will loosen up and get that sloppy feeling again and the wobbling comes back at every bump...until the next time it feels like tightening up and driving right again. I have no idea what to do now. I'm going back to Sears today to have them check their alignment. Other than that, all I can think of is to change the rest of the steering components and check the steering box for malfunction. I hope someone can help all of us Dodge owners out off of the road tested info that I've just provided. Dodge doesn't seem to care to address the problems with their trucks front ends, and we need a solution before people get hurt or die. I was almost run over by an 18-wheeler trying to figure out how to handle the shake. I can't afford to buy another truck. So I need to fix this one so I can keep working. If anybody has a concrete solution to these problems, please let us know. I've read 20 different opinions from mechanics on these blogs, but nobody has said yet that they fixed someone's truck with these problems and have since heard from that customer and everything is still working fine. Opinions are helpful sometimes, but they're also confusing when they're conflicting.

I would check for a broken springs, very common. As for the missing, is there a check engine light on?

most probably a torn lower suspension arm rubber bush that would not show up if the car was on a 4 post hoist
there is a problem there as the noise would not be evident if there was nothing wrong
different tire pressures will give different noise when hit with a tire lever ( a trick used by truck drivers to check for flat/ under inflated tires
good tire solid sound
low pressure tire a dull sound