You should consult with a New York lawyer as your mother was a resident of New York and that's where the Estate was probated. In Florida it would go half to you and half to your brother's children, in equal shares.
The contents of this answer should be considered friendly advice, not legal advice and the answer should not be construed to constitute an attorney-client relationship.
Short answer is that you definitely need to consult with a New York attorney given that this is the state where probate took place. And, you will most likely need to reopen the probate to "properly" distribute this asset (and it will be distributed according to NY laws regarding intestate succession).
My question to you is have you investigated why she received this distribution? Was the policy cashed out? Or, is the policy still existent? If it still exists and insured your mother's life (and the money you found was a dividend or other pay out of some kind), than you should contact the insurance company to ascertain whether she named a beneficiary (which means the insurance pay out would pass directly to the beneficiary with no need for probate). If no beneficiary was named, than the proceeds of the policy would also have to be distributed through probate. Another possibility to consider is that the policy still exists and was owned by your mother but did not insure her life. If that is the case, than the policy itself is an asset which should also be transferred into her estate for probate.
Best of luck to you as you wind your way through this process!