Yeah, Iceman gets written off a LOT for his power level; in the movies he was just sort of a generic nice guy, and in the comics he's more of a joker. Both help deflect appreciation of his potential. Emma Frost, when controlling his mind, was able to really open his eyes to what he could accomplish.

Technically that kid wouldn't be considered a mutant, as there is a specific mutant gene (or something to that effect) that the kid wouldn't have. But there might be some resentment in a sort of "nepotism" way. Like: Spidey actually went through getting bitten by that spider himself; you're just leeching off your dad's powers! There haven't been a ton of kids of altered non-mutant couples to make the comparison with, and the most obvious one really is a mutant who was further affected by his parents' altered physical builds. Another good comparison is with the Runaways: only the child of two mutants, who had the mutant gene herself, was considered one.

That said: between so many writers, over so many years, there's a lot of contradictory material even within these major themes. So I will just try to pull bits into a coherent whole that works for this story. :)