AutoCAD Architecture :: Lines Moving Each Other At Corners

I  am having a problem with moving a line that is attached at a corner to another, as it moves that line as if I clicked on the intersecting snap point at the end of both lines and dragged it. I want to move or copy the line away, but it somehow is attached to the other, and is quite annoying and impossible to work with without deleting and redrawing lines. I've tried exploding them, but they are not joined in that way, and are not "grouped" (I don't think, because when I did "group" them, it made a box around them and highlighted both lines at the same time). A symbol shows that is two boxes, one an outline and the other solid which is up and to the right. I can't figure out what mode it is in to turn it off!