For the question, how to:

move control point 1 to A,
move control point 3 to B,
locate point 4 which bears the same relation to A and B as control point 2 does to 1 and 3.

move control point 2 to point 4.
?

Response:
Create Moi points at mpt1, mpt2, and mpt3, and select them.
Use Orient Line/Line to move mpt1 to A and mpt3 to B. This will move mpt2 to point 4.
Move control point 1 to A, control point 3 to B, and finally, control point 2 to point 4.
Delete mpt1, mpt2, and mpt3.

Is there such a shortcut script?

I would like to be able to set the axis directions in 3D view better. Cannot seem to do it well with right mouse drag of screen.
Set z vertical, y horizontal, and x to the southwest.

- Brian