I plan on leaving my employer for a new job with a two week notice, but a coworker has a vacation planned two weeks after I leave and there is no one else to provide cover. I would think asking to delay my start date with my new employer by a week would be reasonable, but two weeks might not be agreeable.
I don’t want to cause any friction with my new employer, but I also don’t want to leave on bad terms with my current employer. Will I be ineligible for rehire if I were to leave before my coworker takes off for vacation?
This isn’t your responsibility. Your “obligation” (if you can even call it that since its optional) is to only provide a 2 week notice unless the standard is different in your field (for example my mom’s work as a notice that is typical to a month notice, which is written in her contract and she loses a chunk of pay if she fails it)
Other employees vacation isn’t your responsibility, and honestly if your previous work did hold that against you, it isn’t an employer you would want to go back to anyway. I think requesting your new employer waits an additional 2 weeks will look worse on you then if you left your previous employer hanging.