If I'm understanding you correctly, you want to have the "swale-line" layer's linetype be the arrow and dots in both drawings. I also assume the linetype for the layer "swale-line" is defined the same in both drawings (by this I mean the linetype name).
Under these assumptions the easiest way to do this would be to use the RENAME command.
1. Go into the drawing you wish to change, enter the RENAME command and change the layer name "swale-line" to "swale-line_old", change the linetype's name similarly.
2. Exit the RENAME command, QSAVE the drawing.
3. Go into the drawing that is shown correctly and copyclip a line entity that is on the "swale-line" layer and has the correct linetype, paste it into the 1st drawing (after you paste it you can erase it right away).
4. Isolate the "swale-line_old" layer, highlight all of the entities on that layer and change their layer property to "swale-line".
Once you turn on all your layers, the entities should have a new (same as the good drawing) linetype.
HTH,
Rick