Is it permissible to return gold that a mother gifted to her young daughter, despite the mother's dying wish that it not be disposed of, especially since the gold was purchased from the brother's wife, who now wishes to reclaim it?

The gold gifted to your daughter has become her property, and you are not permitted to dispose of it except in a way that benefits her. If exchanging it for other gold is more beneficial for her, then there is no harm in that. The mother's will, which prohibits disposing of it, does not prevent you, as it is not obligatory to implement it. However, if not exchanging it is more beneficial, then you are not permitted to exchange it.