What is the ruling on one who takes money from her brother under the pretext of renting a house, but she does not do that, rather she hoards the money, knowing that her brother will be angry if he discovers the truth, especially since she and her husband have working children and a spacious house? And what should she do with this money, and is zakat obligatory on it?

It is not permissible for the sister to spend the money her brother allocated to her for housing rent on anything else, unless he gives her permission.

If the brother gave her the money believing she was poor and in need, while she is not, then it is not permissible for her to take it, and she must return it to him because it has not entered into her possession.

The sister is not obligated to pay Zakat (definition) on this money; rather, its Zakat is due from her brother, its owner.

If the money reaches the nisab (definition) (threshold) and a hawl (full lunar year) passes over it, then Zakat is due on it, and the brother should reclaim the value of the Zakat from his sister for the period she possessed the money.