I am willing to bet that the plumbing vent stack is plugged, or was capped for the move, or they screwed it up some other way.
Your toilet is draining because there is no ventilation on the other side of the p-trap that is built into the toilet, so when other water goes down the waste line, it siphons all the water out of the toilet. Have someone get up on your roof and look for a 3" thick or so black plastic pipe sticking out of the top of the roof with no cap, hopefully near your bathroom. Make sure it isn't capped, and if you are still having problems, call the nice people who BUILT your manufactured home and have them come out and fix it. THIS IS WARRANTY WORK!!!!