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Couldn't write this up in a comment, so I'll make it an answer instead even though this is a question.

I calibrated my camera and obtain the cameraMatrix and distortion coefficients. I believe they are correct because if I undistort my image it will look good.

I'm attempting to transform image coordinates to plane coordinates in the following setup:

image description

Each black square is one corner of my calibrated surface. I know the image coordinates of each of these squares, in my current calibration they are:

TopLeft: [170, 243]
TopRight: [402, 238]
BottomLeft: [82, 383]
BottomRight: [513, 346]

So, now I want a new coordinate system, so that

TopLeft: [0, 0]
TopRight: [0, 1]
BottomLeft: [1, 0]
BottomRight: [1, 1]

So, now I want to detect objects inside this area, and transform their images coordinates to my [0,0] - [1,1] system.

I used these four corners as input for the cv::solvePnP function and then used cv::rodrigues to obtain the rotation matrix. In this current calibration, these are my results:

translation vec: 

Rotation Mat: 
[0.994295199236491, 0.1037446225804736, 0.02478124413546758;
 -0.05350435092326501, 0.2841225297901329, 0.9572939321326209;
 0.09227318791256028, -0.9531586653602274, 0.2880524560582033]

So, I would think that this would be enough for me to transform any image point inside that area and turn it into [0; 1] coordinates. To test, I tried to make the calculations for the image points that I already know (the corners).

If I try to use these matrices to transform the TopLeft corner [170, 243], I should be able to get [0, 0] result. But this is not what I am getting, so obviously I am missing something along the process, since I know that this task is possible to achieve.