Does opponent process happen in the retina or in the brain?
Opponent process happens BOTH in the retina, and in the brain (Lateral Geniculate Nucleus).

Here is the excerpt from Vision Science: Photons to Phenomenology by Stephen E. Palmer:

In the brain (LGN):  


  Physiological psychologist Russell De Valois (1965) and his colleagues (De Valois, Abramov, &amp;
  Jacobs, 1966) measured responses in the LGN of macaque monkeys and
  discovered color-selective cells whose responses to wavelengths of
  light were incompatible with trichromatic theory but conformed roughly
  to the pattern predicted by Hering's opponent process theory. Some
  were excited by red light and inhibited by green (R+G- cells). Others responded in the opposite way,
  exciting to green and inhibiting to red (G+R- cells). In addition,
  they found cells that were excited by yellow and inhibited by blue
  (Y+B- cells) as well as ones showing the reverse pattern of responses
  (B+Y- cells). Together, these LGN cells can reasonably be interpreted
  as a neural implementation of Hering's opponent process theory.  


In the retina:  


  Further research has shown that these patterns of response are also
  present in the bipolar and ganglion cells of the retina. Output of R+G- opponent cells can be derived by combining excitatory
  input from the L cones and the inhibitory input from M cones,
  essentially computing the difference between the output of these two
  cone systems (L - M).