Should I use my mother's small sum of money to buy her gold, or to build the mosque that I intended, especially since my siblings do not know about this money?

You must execute your mother's agency in disbursing the amount for building the mosque, and your brothers' knowledge of this is not a condition.

You must inform your mother that charity (sadaqah) and spending in the way of Allah cannot be revoked once they have been issued and their conditions met, even if that was before possession, because donations made with the intention of donation cannot be revoked.

Accordingly, it is not permissible for your mother to revoke her donation of the aforementioned amount and spend it on buying gold.