Am I entitled to demand a sum of money in exchange for canceling the lease contract, and is it permissible for me and my daughter to continue residing in the apartment as the tenant if my husband's family refuses any solutions, especially given that it is the only available housing for us?

The rental contract between the questioner's husband and his father should be examined. If it is valid and specifies the duration and rent, then the contract remains in effect until its term expires. The brothers do not have the right to annul it before that time, and the contract does not terminate upon the death of the lessor or the lessee. However, if the contract is void, such as perpetual contracts, then the questioner has no right to remain and must hand over the apartment to its owner or his heirs. She is not entitled to demand compensation for vacating the apartment. If the questioner and her daughters inherit the apartment, she is not permitted to exclusively benefit from it without the other heirs. They must agree on how to utilize the inheritance.