Given the shortage, they may try to accommodate you, but reading your post, one or other of these two, or perhaps a third, will suddenly say they can't manage without you. While I don't doubt their problems, the idea that you are their only solution is unlikely. You are just the one that was easiest to find.
Things happen, life moves on, and they'd better learn that nasty fact, and learn to manage better. They will benefit, and so will you.