Can my employer make me make up time for leaving early due to a parent going in to the hospital for surgery or is this covered by FMLA?

You can take time under FMLA for a sick parent, but it has to be arranged in advance. It's for the care of a relative, not for an emergency situation where you have to rush off. That should be covered under personal leave or some other designation. Find out what the company policy is about that.

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If you qualify for FMLA and you have it approved, you are fine. You have to be out days before you even qualify.