Would it be considered usury for a mother to sell a gold necklace to her daughter in installments at the price of the day of sale, with the daughter receiving the necklace from the first day, and how can they absolve themselves if it is?

The majority of scholars prohibit the sale of gold jewelry for deferred payment, stipulating immediate possession (qabḍ) at the time of the contract, and this is the relied-upon opinion. However, some scholars from the Hanbali school and others permit it, arguing that manufacturing transforms gold from a currency into a commodity. Since your mother and sister were unaware of the ruling, there is no blame upon them for proceeding with the transaction based on the view of those who validate it.