What is the way to please one's mother and settle an old debt owed to an institution, knowing that she refuses to pay it, considering that the family's situation is still difficult under the pretext of wanting to buy a house, and she gets very angry if her daughters spend their money without her knowledge or permission?

If the creditor absolves you from the debt, then it is not obligatory to repay it. However, if they do not absolve you, the debt remains your responsibility and must be repaid when you are able. Your mother should not be obeyed if she refuses to repay it, because obedience is only in what is good, and procrastinating on debt repayment is not among good deeds, as the Prophet (peace be upon him) said: "Procrastination [in paying a debt] by a wealthy person is injustice." You must convince your mother to repay the debt, even if it is through charitable people. If she does not respond, then repay the debt even without her permission, as the Prophet (peace be upon him) said: "Whoever seeks Allah's pleasure by the displeasure of people, Allah will be pleased with him and will make the people pleased with him. And whoever seeks the pleasure of people by the displeasure of Allah, Allah will be displeased with him and will make the people displeased with him."