I just rebuilt the engine and transmission when I apply the brake or try to go into reverse there is a loud popping noise and the hole car vibrates like something is trying to lock up.
Time to rebuild the rear axle.
Like Royce writes, it's time for a rear axle rebuild - it's most likely the babbitt thrust washers besides the differential that has broken from time and corrosion. Replacement bronze thrust washers are available and recommended, but you'll likely find other issues inside when you look into it - the drive shaft would likely need a rebuild too.
Don't drive the car until everything is in order - it'll only get worse and you may loose the brake completely.
Pull the rear axle and fully rebuild it.
Yip, the diff is probably the culprit.
You do not want the pinion gear to disengage the ring gear....
Hope this helps,