Is it permissible for a mother to include two apartments from her properties within the father's inheritance, designating them for her two daughters on the pretext that they are their share of the inheritance, and refusing to give them other apartments, justifying this by saying that the two daughters are married and that their father had spent on their marriages?

What your father bestowed upon your mother during his lifetime, with his consent, is her exclusive property and does not enter into his estate. Your mother must be just among her children in giving gifts, with the male receiving the share of two females. If she does not do so, then she must either give to the remaining children or reclaim the gift. Your being a married woman and your father having provided for your marriage does not alter the ruling; for it is the father's duty to marry off those whose maintenance is incumbent upon him, and this has no relation to inheritance or gifts. This is provided that the gift was genuine and your mother took possession of it during his lifetime; otherwise, it would be a bequest, not a gift, and the properties would be returned to your father's estate and divided among the heirs.