Employment Law Questions? Ask an Employment Lawyer.
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Absent you having a written contract for employment with the employer or a union contract, you are an at will employee, which means that the employer can decide when they need you and when they do not need you. Which means they can insist on when you need to be at work and the hours.
HOWEVER, under the Family and Medical Leave Act, you are entitled to reasonable accommodations for caring for a family member with a qualified condition. This would be a qualified condition and what you need to do is put together a written request that specifically states you are requesting leave under the FMLA for the purpose of taking care of your son with his qualified medical condition and you need to include medical reports from his doctor and his school that nobody else is available to care for him on that day and you need to ask for time to leave work under FMLA to care for that child.
If your employer denies you that leave or retaliates against you for submitting such a request, then you have grounds to file a complaint against the employer to EDD and the US Department of Labor for violation of your rights under the FMLA.
FMLA can be used for intermittent care of a family member with a qualified medical condition, so that is what you are seeking.