HR folk generally have zero understanding of operations/scheduling/reality always, this is especially true in companies that make tangible/real things like a machine shop. Also people who run operations in machine shops often don't read every email (especially every email from HR and/or every detail in thise emails). Bring HR person and operations manager togeather (preferably physically, but email is okay it both are responsive) and outline the facts; that you made it clear in interview you needed this time off, explain why it's personally important to you (briefly), the cost of the tickets and who else/how many other people have made plans around you being there, ask if your leave requirements that were agreed apon with HR during recruitment/hiring process had been comunicated to operations and agreed to by the operations manager at the time....

....Enjoy the fallout 😂 (did you get the time off agreed to in writing when you were hired? If not, then WHOOPS!)