Am I doing this wrong, with the no trespassing on the door?

Also, could your door be backwards? Try setting it to block someone in your household and see if they can come in. If they can, go into build/buy and flip the door so the arrows point the other way. (I think doors and windows are supposed to point outwards. Some of the styles make it difficult to tell.) Now try to lock it again. If it works that might have been your problem and the No Trespassing lock should work now.