Must one forgive a younger, non-pubescent brother (11 years old) regarding a right due to him, knowing that I had given him some money?

The forgiveness of a discerning child regarding a right due to him is not valid, because it is an act that is purely detrimental to him. As stated in the Kuwaiti Encyclopedia of Fiqh, the purely detrimental acts of a discerning child—which are those that result in something leaving his possession without an عوض (compensation), such as a gift or charity—are not valid from him and are considered void, even if the guardian approves them.