Check if polygon is inside a polygon
Perform line intersection tests for each pair of lines, one from each polygon. If no pairs of lines intersect and one of the line end-points of polygon A is inside polygon B, then A is entirely inside B.
The above works for any type of polygon. If the polygons are convex, you can skip the line intersection tests and just test that all line end-points of A are inside B.
If really necessary, you can speed up the line intersection tests using the sweep line algorithm.
First check that one of the corner points in the polygon is inside the other polygon using the script. Then check if any of the lines in the polygon crosses any of the lines in the other polygon. If they don't, the polygon is inside the other polygon.
Is the polygon convex? Because, if it is, you could just run the "point in polygon" script for both "corners" of your "rectangle." If both corners are in, and the polygon has no "curves" inward, then wouldn't the whole rectangle be in?