Is it permissible for the testator to stipulate in his will that the share of his wife and minor children from the inheritance be handed over to her to dispose of without recourse to the courts or the حسبية (guardianship) prosecution, with a recommendation to fear Allah concerning her and the minors' money, and not to dispose of it except out of necessity, or to grow the money, or for their education, and on condition of seeking sharia opinion?

It is permissible for you to entrust your wife, after your death, with the care of your young children, the preservation of their wealth, and its disposition in a manner that serves their best interests, and similar matters that do not contradict Islamic law. This is because the meaning of an entrustment to a person is that you grant them the authority to act, after your death, in matters you used to manage. This includes settling debts and recovering them, distributing bequests, and guardianship over minor children. An entrustment to a woman is valid by the agreement of most scholars.