Is it permissible for children to resort to legal action to claim their share of an inheritance in order to pay off their deceased father's debt, if their mother refuses to sell the father's property to settle the debt?

We advise you to fear Allah and mend your relationships, and to try to convince your mother gently and kindly to pay off your father's debt from his inheritance, explaining that real estate values may decrease, and that the deceased's soul is tied to his debt. If she does not respond, then there is no objection to resorting to courts and laws.