Is it necessary for a mother to resign from her job to care for her young son, especially given his distress from her absence, or will he adapt over time?

If there is no necessity for work, it is obligatory to leave it. Early retirement can be resorted to if available, and staying at home to care for children and parents is the original principle, and it is not permissible to deviate from it except out of necessity. Raising children is priceless.