A few weeks back I was having a problem with my 2007 GMC Sierra Classic Z71 intermittently have a really bad vibration when almost to a complete stop. It was on dry smooth pavement. The vibration was horrible. Very intense shaking of the whole truck just a split second before a complete stop. Finally figured out that whoever replaced the rear brake shoes last, did a sub-par installation. They had cut through the rubber boots on both sides of the brake cylinder on the passenger side. That wheel cylinder was leaking and for some reason getting bound up inside the drum to the point it was making the brake shoes get jammed/stuck on. I changed out the brake cylinder on the passenger side and the brake shoes on both sides. That fixed it! Brakes are smoother than ever even after towing a grossly overweight trailer with a 10,500 lb F**D Superduty diesel 4x4 on it! Hopefully this helps someone.

 

i get dust in the drums on my ranger. when it's wet outside it makes them grab hard. i'd guess you're dealing with the same issue and by the sounds of it, the drum might need turned. i'd turn the drum and see if that helps. warped rotors and drums are more noticeable at lower speeds.