This paper analyzes the "AI Dynastic Trap," focusing on how parental technological history affects human capital investment during periods of rapid automation. We examine the household decision to divert effective learning time toward immediate-return tasks that fail to build resilience against obsolescence. Using an overlapping-generations model with endogenous preferences, we show that parents entrenched in traditional sectors tend to underestimate skills obsolescence, thereby locking their children into a cycle of digital vulnerability. However, the model identifies a "Dynastic Break" phenomenon: a threshold where technological polarization becomes so extreme that it overrides cultural inertia, forcing even traditional households to prioritize deep literacy.

We conclude that modern inequality is driven by a "digital adaptation divide" transmitted within families. Therefore, effective policy must go beyond subsidizing education to focus on altering intergenerational adaptation norms among parents.