Is the money left by the mother, which she designated for her two daughters as compensation for the sale of land whose full price was taken by her son, considered their private property equally, to the exclusion of the son? And do the children of the deceased daughter have a right to it, given that there is another known inheritance?

This gift is invalid because it is contingent upon a condition, and a gift does not accept contingency. However, Sheikh al-Islam Ibn Taymiyyah was of the opinion that a gift made contingent upon a condition is valid if the gifted item is taken possession of by the donee before the death of the donor. If possession is not taken before the donor's death, the gift becomes void. Therefore, you both are only entitled to your share of the inheritance. In the event that the gift to the two daughters is not valid, they are entitled to take from the inheritance an amount that equalizes them with the son, unless the son was specifically given the gift for a legally recognized need. As for the children of the deceased daughter, they have no right to the gift, nor to the inheritance, because they are excluded by the direct male offspring.