Is a mother required to spend on her children if she has an income, given that she refuses to buy anything for them except what she likes, and demands that they buy things with their own money, knowing that they have money designated for expiations, which they do not own, and they buy with it when it is available?

If the children have no money or earnings to suffice them, then the affluent mother is obliged to spend on them. If the questioner has enough money for her own expenses, then her mother is not obliged to spend on her. Nor is she obliged to spend her money on expiations (kaffarat) as long as she needs it for her own expenses; rather, she should expiate by fasting. For expiation becomes obligatory from wealth that is in excess of one's essential needs.