I'm picking up a lot of fear in that picture. In their body language, their faces, they way Shinji asked if she's "really okay." The placement is a bit ambiguous but both of them either have sweat or tears on their faces. All that has me trying to rewind the story in the picture. What happened 30 seconds ago? The elipsis in Asuka's answer tell me that she is unsure. She is ASUKA FREAKING LANGLY! The Second Child. The warrior that Spartans(your choice which ones) and Klingons salute! And she's not sure about holding a baby? This isn't the scene in a happy home. Or at least it is a happy home, but this is a bad night.
All that said, it's a wonderfully composed, powerful image that hit me right in the gut and left me with a very visceral reaction.
I can see what you are talking about from your perspective, if it was a stand alone picture.
With Gendo, Yui and Shinji, I see a upset Shinji and a frustrated Gendo, with Gendo passing off the brat-I mean his dear son, to Yui, who knows what the fuck she is doing.
With the Shinji, Asuka and Junior, I see Asuka demanding to hold Junior. Headcannon for the picture, is normally Shinji gets up during the night to calm and feed Junior. Cause Shinji is Shinji. Asuka decided to take care of Junior this night, why? Maybe she felt bad and Shinji was tired? So Shinji, who is not use to this, makes sure that Asuka is okay with it, and Asuka being Asuka, got a little ticked.
So yeah, that's my take on those pics.
Once again, Rei would not have a S2 engine, because that (the Fruit of Life) is an Adamite function.
...mind, Tabris also had reasoning and communication and so on, all Lilithian stuff (Fruit of Knowledge), so maybe lines blur a bit for seeds of life or for Nephilim.
I always thought of it, that there were two different S2 Organ types. One is the Adamite, fruit of life/power, with the lasers and reality breaking. The Lilithian, fruit of knowledge/individuality, is used for intellect. I always imagined it as a small, grain sized piece, located in the brain.