Multiple things to watch for here. Keep in mind I only know what you reveal in the original post about what you do.
Tripod under the telescope could be inadequate. Star tracker might be overloaded or must be balanced better with the counterweight kit. Polar alignment not quite right. You could be choosing an unrealistically long exposure time for the star tracker's ability. You are touching the camera with your hand as you take the photos (using a remote shutter or self timer mode required), mirror slap during shutter release.
The last point has to be addressed with the camera settings with any DSLR. Mirrorless bodies have an advantage here. I have only used D7000 or better DSLR bodies so I cannot advise on if a D3100 even has a Mirror-up mode (press shutter once to raise mirror, press a second time to release shutter). A way around that is to use LiveView so the mirror is locked in the up position the whole time.
Then there could be the surface you are set up on. Wooden deck could be trouble. Should be firm ground or pavement.
Thanks so much for your reply!
The counter weight was set properly, but the polar alignment was not totally accurate; I was taking pictures in front of my house instead of in my backyard so I pointed the tracker in the general direction for the north star. The tracker did track the moon fine, never drifting out of the frame.
I did have a cable release hooked up to my camera on a 2-second delay, but also noticed that the strap at times was causing some motion from swaying. Exposure times varied between 1/15th to 1/125th with exposure compensation on some shots.
I did finally try the mirror lock-up function, but tried to refocus the shot in Live View mode which made it worse. Couldn't get the focus back to where it was and then just gave up for the night.
I also was using a T-adapter on my camera to connect to the telescope; don't know if that had any affect on the focus. Will try not using the T-adapter next time to see if that helps.
Thank you for your suggestions!!