2001 rear end noise

I have a 2001 chevy Z71 1500, I hear a clunking noise when I accelerate from a stop, also when I pull my race trailer it feels rather odd in that there is a slipping feeling for a brief moment almost like starting out in the mud then hitting the pavment. I have seen some posts about transfer case fluid needing replacement to fix the problem. The thing is that if when pulling the trailer and I accelerate slowly then the effect is significantly reduced almost to the point of non exsistance. Any ideas?