Is it permissible to give female siblings a portion of the non-fixed return from a saved marriage fund to help them with their trousseau, and is it permissible for the mother to use a portion of this return for household expenses or to buy gold for herself?

The questioner wants to dispose of the bank's earnings out of piety and caution, and there is no harm in this, as the unlawfulness of these earnings is not definitively established as long as the bank is Islamic.

It is permissible to give this money to sisters and the mother as charity or a gift, and there is no harm for the mother in using it for household expenses, buying gold, or other permissible matters.

For what is best and most cautious, it is advisable to seek a reliable Islamic bank to deposit money, as the transactions of government (Islamic) banks are subject to significant doubt.