I didn't know they worked 250 miles apart. While you can't guarantee that they don't see each other, or come in contact with each other, you can certainly minimize their opportunities. I still say she should look for another job. Consequences.
As for your kids, you have already told them what was going on, and what you required of their mother for you to stay. They're smart kids; they can do the math if she goes. If asked a direct question, give them an honest answer. But don't INITIATE those discussions with them when there's nothing new to add, as it will only add to their anxiety level.