What is the ruling on disposing of money that was a trust held by the father for the children of the questioner's uncle, which the father spent without the knowledge of his heirs, and then his heirs repay it to the uncle's children in installments without informing them of its true nature? And is it permissible for the heirs to dispose of it in ways other than the rules of inheritance, given the inability of the uncle's children to manage their own money?

The uncle's money transferred to his heirs and must be paid to them in full. You erred by distributing it without observing the rules of inheritance. This mistake must be corrected while concealing your father's action, and a will should be written for the remaining amount to ensure the right reaches its rightful owners. Your father was not permitted to dispose of this money because it was a trust (wadi'ah). The duty was to settle this debt before dividing your father's estate, in accordance with the saying of the Prophet, peace and blessings be upon him. If your father did not leave enough to cover the debt, you are not obligated to pay it on his behalf, but doing so would be an act of filial piety. If you intend to pay but cannot do so in a single installment, then fear Allah as much as you can, and you are not required to inform your paternal cousins of this.