Truck pulls while pressing the brakes

Hi guys I've got a 2001 Toyota Tacoma PreRunner SR5 3.4 V6 DC stock motor, trans, drive shaft, diff, but bigger tires than the door sticker tells me was on there. When riding down the road the whole truck will shake pretty heavily, starting around 45mph as a small vibe then at 60 it goes up to a pretty steady shake, the steering wheel will also move from side to side as if one of the tires' bands has separated. When slowing down using the brakes my steering wheel pulls to the right side along with the truck moving to the right. My tires have ~15,000 miles on them they are Goodyear wranglers size 265/70R16. I am going to have them re-balanced but I don't believe that them being out of balance would cause it to pull. I snapped some lug studs off a while back, when I pulled the wheels off to replace them I checked the brakes and they all had plenty of life left in them there was no gouging in the rotors or drums and the pads were flat with about 1/4 to 1/2 inch of material on them same for the rotors. Could it be that they need replacing or rebleeding? A bad ball joint? Thanks for the help I know TW will be.

 

i have an 06 and mine does the same thing however to the left... my tires are a little out of balance but i know that (havent gotten my balance done in a little while) i have the 5100s set at the highest setting with stock uca's so the alignment is as close to perfect as we could get it with the limiting uca's but it pulls noticeable to the left when comming off the freeway and pressing the brakes and less noticably when coming to a stop at a stop light coming down from around 35-40. nothing that worries me just a little annoying

 

Shaking sounds like a balance problem.
Pulling sounds like an alignment or brake problem.
Do the brakes pulse when stopping if so warped disc.