the woman who my grandfather lived with will not provide my mother who is the next of kin the information for his lawyer so we can settle his will.

This happens often.  You or your mother can apply to the surrogate of the county in which your grandfather died to be the administrator of his estate even if you do not have a will.  You will be asking to have the estate listed as "intestate" (without a will) and you will ask to have your mother, appointed as the administrator.  The probate clerk in the surrogate's office can help you.  This will give you the authority to get information from your grandfather's bank and get the money back if she emptied the account.  If she has a will, she will have to produce it, otherwise your mother will be in control of the esate. She will also have the right to get his things out of this other woman's house.