Lord Rama was surprised to encounter Lava and Kusa who challenged his power unknowingly before Ashwamedha Yagam.
Why did he not bother to inquire or keep track of his children's progress for so long in their childhood after leaving them in Valmiki's Ashram? As a king it was too easy to find out at least about their education and welfare.
Was he so heartless because doing so conflicts with his royal duty or with his compromised image based on people's expectation? For most of us Rama is a role model.