Is it permissible for my uncles to claim their right to a new inheritance after they relinquished their claim to the previous inheritance, given that there is a waiver document that does not clarify whether the waiver pertains only to the previous inheritance or to inheritance in general? And is it permissible for me, as a representative of my father's heirs, to give any objecting heir their share based on my testimony?

The heirs have the right to claim the new inheritance and take their share of it, because the initial waiver, if it pertained to a specific, known inheritance, does not extend to what is newly acquired from inheritance. Even if they waived the apparent inheritance, such a waiver is a gift, and they have the right to revoke it before it is taken possession of by the donee. A gift is not binding until it is seized, unless it is already in the possession of the donee, in which case it becomes binding simply upon offer and acceptance. The father's share of the new wealth is given to his heirs and remains his property.