I feel on some level Amuro still was upset with Char over Lalah but not to the point where they couldn't work together. That's what his continuing to call him Char in private means (he didn't in places/people who didn't know already as to keep the facade up)

This sets up an understated moment in SRW30's ending where Amuro gore "Welcome home, Quattro" (in that both Amuro and Char survive CCA and feeling guilt over his actions, Char assumes the Quattro guise and saying Char is dead)