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?
I wouldn’t be concerned about that. Businesses are strongly discouraged from badmouthing former employees unless you did something explicitly terrible or criminal. Worst case scenario is they would give no comment if given as a reference.