And ISTR from the chapter that Gendo hates Dorothy, and Rei was pretty much telling him, "You don't like R. Dorothy Wainwright? I don't like oniisan being in danger. Guess neither of us are getting what we want today."
Yo.
That line was two-fold. One, you hit the nail on the head. Rei was being mean because Gendo made a call she disagreed with.
Gendo watches anime with his kids because he's actually trying to be a -dad-. He just happens to have favorites, and he has least-favorites. It's unlikely to be expanded on further in the 'fic, unless I can shoehorn an excuse, but Gendo's favorite anime is Big O, because he admires Roger Smith and Norman. His least-favories, however, include R. Dorothy Wainwright.
That one of his least-favorites is a canon-Rei-expy was a bit of ironic humor I could not resist. A bit of 'there but for the grace of God go I', if you will.
As to Pacific Rim....anybody ever get the feeling that movie took a -whole fucking lot- of cues from Evangelion?
1) Giant humanoid mechs vs. inhuman aliens with no two the same at all?
2) Giant aliens dissimilar from one another in wildly-different ways, but there's -one organ- they all possess that is, in fact, -exactly- the same between creatures?
3) Pilots mentally sync with mechs, and personal triumphs or tragedies affect the success of this sync-ratio.
4) Main character lost a close family member to one of the mechs. Sure, it was in battle and technically a kaiju, but still.....
A whoooooole lot of similarities. If there had been an abundance of Catholic crosses in the Shatterdome (another similarity! Special massive facility! Geofront=Shatterdome) I'd have honestly wondered if Pacific Rim wasn't a modernized attempt at an RL adaptation of NGE.
EDIT: Why am I playing golf, and what's that between me and the sun? Odd, that....