Is it permissible to indirectly take the value of housing rent from the company, after its owner broke his promise to pay the rent for the employee who brought his children, despite him providing for other employees who have families?

Your entitlement to a family housing allowance depends on the contract between you and the company. If the contract does not stipulate this, then reference should be made to labor law and its regulations. If your entitlement is proven, you have the right to claim it and appeal to the responsible authorities. As for taking the allowance by stratagem, this falls under the category of seizing a denied right, and scholars have differed on its permissibility. However, it should be noted that the point of contention in seizing a right is when the right is genuinely established. The promise of an official does not establish a right; rather, what is stated in the contract or the system's regulations is what matters. Regarding the issue of a promise, if the person to whom the promise was made suffers harm due to the non-fulfillment of the promise, then the promisor is obligated to compensate them for the extent of the harm.