Does my mother's mother inherit one-sixth of the house, given that the money was from my mother's work, or one-sixth of my mother's share of her husband's inheritance? And what is the ruling on her waiving the inheritance?

It is advisable to treat the grandmother kindly. The wife's salary and possessions are her private property, and she is not legally obligated to spend anything [on others]. If it is proven that the house was built with the wife's money and registered in the husband's name, then it should be examined whether it was a gift conditional on possession and قبض (formal taking of possession). If that was fulfilled, it becomes the property of the husband and his heirs; otherwise, it is an inheritance for the wife. Mere registration does not constitute ownership. It is advisable to refer the matter to a judge. The grandmother inherits one-sixth of her daughter's wealth if the house belonged to her daughter, and one-sixth of the price if it belonged to the father. The grandmother's waiver of her share, while she is in good health and the recipient takes possession, is valid. However, if it occurs during her terminal illness, it is considered a bequest (وصية) limited to one-third [of her estate]. Inheritance matters are serious and should be referred to Sharia (definition) courts or discussed directly with scholars.