Are daughters entitled to claim a share of the inheritance from their father, and a share of the inheritance from their mother after her death?

We understand from the question that the father was only renting the house, and that the sons, but not the daughters, bought it. If this is the case, then the disposal by the mature sons of the house they own is valid. If they gifted it to their mother, and then the mother subsequently gifted it back to them during her lifetime, and they took lawful possession of it, then this is a valid gift. However, she should have dealt justly between her sons and daughters in this matter.

However, if the mother did not gift the house to her sons, but rather made their disposal of it contingent upon her death, then this is a will to an heir. Consequently, the mother's action is not legally binding, and if she dies, the house becomes an inheritance in which every heir has their legally prescribed share, according to the hadith: "Indeed, Allah has given every rightful person their right, so there is no will for an heir unless the heirs wish it."

Regarding the daughters' demand for their share of the inheritance from their father: if the father left behind wealth other than the house, then they have the right to demand their share. And if their mother left behind wealth, including the aforementioned house—in the case that it was not a valid gift taken possession of by the sons during their mother's lifetime—then they also have the right to demand their share from their mother's estate.