Is it permissible to enroll in a vocational school to financially assist an ill mother, or is it obligatory to work to provide for all her needs?

Allah Almighty commanded beneficence towards parents, and among the obligatory forms of beneficence is spending on them if they are poor. So, if your mother is poor and unable to provide for her expenses or treatment, and you are able to provide that through permissible work, then you must work to meet these needs. This is because working to fulfill your needs or the needs of those whose maintenance is obligatory upon you—such as your mother—is a duty, in accordance with the Prophet's (peace be upon him) saying: "It is sufficient sin for a person to neglect those whom he is obliged to support."