Hi
With this issue, i would first inspect your Carrier Bearing, its basically the bracket that is located in the centre of your prop shaft underneath your car (the big drive runs from your transmission to your rear differential)
It has a bearing that keeps your prop shaft running dead centre, but common for the rubber around it to perish or to get worn and cause some play/movement under acceleration or load.
My money would be on this
Hope this helps!
Mal