1996 Tahoe Differential Problem?

My vehicle recently started to make a loud thud when I stop and accelerate. Sometimes it does it real loud then sometimes if I am carefull with braking it does not do it. I took everything out of the tahoe to make it was not a tool inside rolling around in the truck. I checked my spare to see if it was secured on tight.
I noticed it started after I pulled a 16ft. Trailer with only landscape debris. I checked the fluid in the differential. I have checked all the motor mounts and transmission mounts. The u-joint look okay, but do have a little bit of play when I put it in neutral and twist the shaft. I did notice that there was some play in the axle shaft when I check my brakes and tires. How much play should there be?

My transmissions shifts fine, and it does not make the thud noise when I put it in reverse. I have put the truck on a lift and had it running to see if I can see the transmission or motor shifting from bad mounts, but everything looks solid. The only thing I noticed on the tranny is area where the drive shaft inserts into the tranny is a bit wet, not to the point where it creates a puddle of oil. Any help Please.

Gilbert
Odessa, TX