It is required that the executor administer the Will according to its terms. The problem you have now highlights the danger of not periodically reviewing one's estate plan. Things may have -- and most likely have -- changed dramatically with your mother's family and the charities she loved in the two decades since she made her Will. I'm sorry your situation is illustrative of the need for periodic reviews of Wills and Trusts. Best of luck to you.
If your mother has passed away those donations have become vested and must be distributed. If there is a will (not a trust), it will have to be filed with the probate court and everyone named in it will be entitled to notice. They will then be entitled to their share at the end of the administration. There are no options to not pay the bequests in a will after they have vested (after the maker of the will has died). I encourage you to have a probate attorney assist you through the process.
Is your mother still living? Did your mother die? If your mother is dead and probate is necessary, you would have to give notice to the charities and the secretary of state of the probate. Then upon order of distribution you would have to file receipts. You would be violating a court order in not making the distributions.
If the assets were not subject to probate, in a trust or in joint accounts or accounts with beneficiaries, the will is not relevant and does not control.
If your mother is living and has capacity, she should change her will. If she lacks capacity and you can prove her intent is otherwise, you could seek to change the Will through a substituted judgment proceedings.
It sounds like the estate is large enough to hire an attorney. Regardless of the facts, you would be wise to do so.
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While I am licensed to practice in New York and California, I do not actively practice in New York. Regardless, nothing said should be deemed an opinion of law of any state. All readers need to do their own research or pay an attorney for a legal opinion if one is necessary or desired.