To what extent is it valid to approve the waiver of a share in a property in exchange for a debt, despite a prior and documented agreement between the son and his deceased father guaranteeing the son a share in the property in exchange for his financial rights?

If your father intended to sell you a portion of the property in exchange for your money that he had, then you own that portion, and no one has the right to take it except with your permission. As for your acknowledgment that your money with your father was merely a debt, it has no effect, as long as you were coerced into it according to Islamic law. And among the forms of legitimate coercion is insistent pressure from someone who holds influence over the coerced person. Therefore, your acknowledgment under your mother's pressure is invalid and does not forfeit your right to the property if you can prove it with evidence.