You should talk to the attorney handling (mother's) probate. If the father's probate had been done properly, his name should have been off back then.
If the father and mother held the property with survivorship right, mother could have filed the death certificate (and the will and probate would have not applied to the property). If they didn't hold ownership, the probate process should have had the estate prepare an appropriate deed to mother. Filing a death certificate now isn't going to affect any of this.