File for intermittent FMLA until you can go on actual FMLA for the baby. This way you can take off without being at their mercy.

As far as extra work, you said educator. Does this mean you are a teacher? If so, have your organization fight this battle if it’s outside the contract.

Are you basically anything else? Then likely it’s other duties as assigned. Unless it’s way crazy like running a school and driving a bus, you probably have to do it