The critical fact is where mother was domiciled at the time of her death. If NY, then you will nedd to do an ancillary proceeding and if VA, then you nEed to do an administration oR probate proceeding..the determining factor of who owns real property is the deed, not the tax bill. However, if your father predeceased, perhaps the deed was never changed to your mom's name. Consult a lawyerr.
Ms. Siegle is correct. You should consult with a probate attorney where your mother resided at the time of her death for fact specific guidance in processing her estate.
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Your summary is long on potential issues and very short on facts. An attorney needs to review the DEED for the property to find out if your mother owned it, or it was owned by her estate and your grandfather's estate. That will determine if you have one or two estates to probate. If you have other siblings or if our mother was married at the time of her death, then things get much more complicated. I would have an attorney review this, right away. (A Virginia attorney would be best.)
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You're not going to be able to sell the land so quickly. When your mother died, did you go through the Surrogate's Court in Kings County (Brooklyn) to finalize her affairs? I work here in Manhattan with a lawyer who is also licensed in Virginia, so we can help you figure this out.