I don't see why Teen Gohan getting a rage boost in Super Saiyan 2 necessitates Kid Gohan having one (that's nebulous beyond the obvious increase) as well.
If you buy that rage boosts bring out Gohan's potential, all you need is SSJ2 was his full potential back then, now it's increased. According to Elder Kaioshin, Gohan has a huge amount of untapped potential. If he didn't, I could buy the kid Gohan (unrelated to SSJ2) rage boost.
Besides, Gohan was ready to lay the hurt on Cell after he came back, despite not looking particularly like an angry person, same goes for when he actually kills Cell. He obviously lost this supposed secondary rage boost when Goku died, and he realized that his aimless fury was nothing but destructive. What, he gets it back just by putting on a serious face and flaring his aura? He needed scream and start crying the first time. He smirks confidently while maintaining this rage? He's surprised that Cell can deal so much damage to him when he loses the most important part of his power? He certainly wasn't angry when he jumped in front of Vegeta, yet it's not his lack of anger that results in his injury, it's Cell's power.
Also of note is that Goku isn't telling Gohan to get angry again during the beam struggle, just to stop holding back and let his power explode.
Rage boost version:
"I'm doing my best, dad!"
"Get pissed you little brat! Kick that fucker's ass! Remember Icarus? He did it!"
Manga version:
"I'm doing my best, dad!"
"Stop holding back, Gohan! Let your power explode!"
Does this line make sense?
"Doesn't Vegeta helping out make you even more angry?"
Gohan's power increases when he gets angry, that's all I got from Vegeta's comment. Super Saiyan 2 was certainly a power increase.
I just don't buy his secondary rage boost being maintained through this entire complicated struggle. All he needs is to use all of the power he unlocked through his anger: the power of his Super Saiyan 2 form.
I could also say I don't understand what the point of his transformation is supposed to be. it just distracts from what's actually going on, apparently. What was the point of all the buildup to "surpassing Super Saiyan"? I realize Goku never said anything about that, but I don't think he needs to. It was the point of the whole arc.