Is it permissible for my mother-in-law to spend the fidyah on me and my children, given that my salary is low and does not cover my expenses?

If your salary is low and insufficient for your needs, there is no harm in your mother-in-law giving you and your children what she owes in fidyah for fasting; because the recipients of fidyah are the poor and the needy, and you and your family are among them.