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 feel like the time to worry about this would have been before you set a start date. At this point, it’s unfortunate, but your new and old workplaces just have needs that are in conflict, and it’s probably smarter to prioritise the new one. Maybe loop in the coworker, see if there’s some kind of approach that works best for them?
The other commenters are correct that on paper you have no other obligations, but not everyone hates their workplace and coworkers, so I think there could be room to be accommodating here if you can.