Non-native speaker here - I don't completely get your description. Maybe a picture would help.
The base plate should never move under normal load, and if it does, it usually is a rot/structural issue in my experience.
Does this always happen, and is it always at the same location where you load/unload the camper? A little flex is normal, especially if the ground slants slightly to one side. Most of the load is on the front jacks, and the camper front usually tries to turn to the "downhill" side when it is not completely level side to side.