First, you only need two points to define a rectangle (unless it's angled). Take a look at it and you'll see that some of the points (corners) in the rectangle have the same X or Y coordinates.
Code:
(X1, Y1)
¤-----------------+
| |
| |
| |
| |
| |
| |
+-----------------¤
(X2, Y2)
Assuming Point 1 is always the upper left corner, and Point 2 is always the bottom right corner, this will check if Rectangle 1 is completely inside Rectangle 2:
Code:
if((R1.X1 >= R2.X1) && (R1.X2 <= R2.X2))
{
if((R1.Y1 >= R2.Y1) && (R1.Y2 <= R2.Y2))
{
...
}
}