What is the ruling on selling a house left by the deceased father, given the mother's desire to sell it and buy a smaller house, along with a dispute among the children regarding the division of the price, the desire of some heirs to take their share, and the mother's desire to take half of the price according to Belgian law, while attempting tax evasion by registering only half of the price?

Your mother is entitled to one-eighth of your father's inheritance, and it is not permissible to request any other division, whether more or less than that. You must explain this Sharia ruling to your mother, emphasizing the prohibition of transgressing Allah's boundaries, and that acceptance of Allah's حكم (judgment/ruling) is a matter of creed. It is not permissible to resort to man-made courts, but rather to trustworthy Islamic centers. If there is an heir who wishes to receive their share, they are entitled to it, and whoever wishes to forgo their share in favor of their mother may do so. You must provide suitable housing for her. It is not obligatory to purchase a house for her from your private funds unless it is a voluntary donation, but you must assist her in securing housing if her own funds are insufficient. You must be diligent in honesty in dealings and avoid deceit and fraud.