I recently moved to another house...Is the tub suppose to wobble or is it suppose to be evenly balanced?

The tub has stabilizers on it ... remove rear panel and make sure the shocks are still attached and or not broke... if all this looks good is the unit on a pedestal if so there have been alot of problems with lg washers and pedestals.... i know your saying well they sell them with the washer as a optional feature ,but they have been giving fits to lg for the last couple of years.... if the shocks look good then most likely you have a bad hall sensor located also in the rear of machine on the part called the stator .the stator is a round device that attaches to the rear of tub and has a copper coil that goes around the entire thing... on this device is a white plasetic device called a hall sensor that measures the spped and balance of unit if unit starts getting out of balance the hall sensor will slow machine down.... good luck to you