The answer depends on the terms of the Will. If the Will provides directly for a distribution, this would be done by the personal representative of the estate. I think your best bet is to have your father review the documents with an attorney to determine how to proceed.
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Any distribution within will of course be determined by the terms of the will. With regards to the procedure of such payments, look to see who is listed as the "Executor" (sometimes called personal representative) of the will - this person is responsible for disbursing the estate. Generally in a will this person will be identified very early on in the language. As executor this person does have a responsibility of carrying out the directive of the will. Similarly, the duty of such is fairly high and these individuals are expected to act with the upmost honest and impartiality. Good luck.
The Personal Representative is responsible for distributing any probate assets according to the terms of the will.
Your question sounds like she named your father and the two cousins to receive the money with the intent of having them split it. If she did not specifically name others to receive the money then you are at the mercy of them to follow her wishes but they do not have to.