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?
It’s your employer’s responsibility to ensure that they have sufficient people trained (or at least their responsibilities documented) so that someone else can pick up the slack during vacations, illnesses, accidents, family responsibilities, etc. If your employer hasn’t been doing that, that’s their problem, not yours.
During your final two weeks, your employer should be asking you to help train your replacement, or at least document your job to help your replacement. Plus there’s an additional two weeks for your coworker to help train your replacement after you leave. Four weeks of training should be more than sufficient to get your replacement comfortable enough to handle everyday tasks, and they can bring anything they need help with to your manager.
This situation isn’t your problem to solve.