“It’s none of their business” isn’t actually true if they are paying. It is your life, but also their money. Q1 - could you add the pre-med classes with your current major without extending your graduation date? Q2 - Coukd you add a minor in Chem and complete the premed classes without extending your graduation date? Q3 - If you switch your major to chem, can you still graduate on time? Could you get a CS minor if you are well underway already in the coursework?
Note that if you don’t get into med school, the job prospects in chemistry with just an undergrad degree are fairly dismal. You might want that CS degree or minor to fall back on.