Is the mother entitled to request a portion of the money inherited by the children from their paternal aunt, knowing that the mother has estranged her son and refused reconciliation unless her request is met?

The contract between your father's paternal aunt and your father, paternal uncle, and paternal aunt is either a valid sale with the condition of gifting the house, or a fictitious sale intended as a gift. Both are valid, but the condition is void. However, drawing up a gift contract for you with the condition of not benefiting from it during the lifetime of the donor is void, because it is in reality a will, so drawing up the contract has no weight as long as the disposition is conditional upon death. Your father's share of the property is an inheritance to be divided among his heirs, including his wife. The matter must be presented to the Sharia courts. Your severance of ties with your mother is forbidden, and you must maintain kinship with her, not raise your voice at her, or argue with her. She must accept the court's ruling regarding the inheritance, and you should maintain kinship with her through money and kindness.