What is the ruling on acting in this situation, taking into account the brother's resorting to mortgaging the family home and his failure at work, and will this lead to the mother and the rest of the siblings losing the house?

The questioner is advised to turn to Allah Almighty and to increase remembrance of Him through glorification (Tasbeeh), seeking forgiveness (Istighfar), and sending blessings upon the Prophet. This is based on Allah's saying: "Verily, in the remembrance of Allah do hearts find rest" and "Seek forgiveness from your Lord; indeed, He is ever-forgiving. He will send down upon you the sky, abundant in rain, and will aid you with wealth and sons." It is also mentioned in a Hadith that whoever dedicates all his supplication and blessings upon the Prophet, his worries will be relieved and his sins forgiven. Most importantly, the questioner must repent to Allah Almighty from the usurious loan, as usury is among the major sins. Allah has promised those who repent ample provision and increased good, as He says: "And [commanding you], 'Seek forgiveness from your Lord and then repent to Him, and He will let you enjoy a good provision for a specified term and give every possessor of grace his due grace.'"