Is it obligatory to include the money that a father gave to his daughter—along with his will to conceal it from the rest of the family—within the inheritance?

The aforementioned amount should be returned to your father's estate, regardless of whether he authorized you to manage it or gifted it to you during his death sickness. This is because such a gift is not valid and is considered in the same category as a bequest (waṣiyyah). A bequest to an heir is not valid unless the rest of the heirs approve it, based on the Prophet's (peace be upon him) saying: "Indeed, Allah has given every rightful person his right; so there is no bequest for an heir."