I don't think Nes needed to apologize for what he said. Not one bit. I agree with what Nes said on the last page. If he were personally attacking his mother that would've been a different issue; because the issue is about her lying and not about her. To me, Nes has every right, and all the time in the world, to be upset. The mother had made a poor choice, but she's making it right by telling Nes the truth.
Good for Nes for having the maturity to apologize like that, and his mom does raise a good point.
I have a critique for the panel with the mom too, though: I think the yellow/orange is too intense, too bright. It's kinda distracting and little hard on the eyes. For a moment like this, I think you need something more subtle.