2005 chevy 1500 4x4 differintail noise

differintail pops when shifting between 1st and 2nd and 2nd to 3rd. have removed cover and the ring gear and pinion are tight but there seems to be slack in the spider gears or limited slip parts. with my foot on the brake and someone looking at the drive shaft it moves about 1/4 of a turn or maybe less. the dealer says there is no problem but i know different. just not sure which parts to replace. or how to force gm to warrenty. any help would be great .