I would think once they're separated, the mites would go away...either disperse, die off, etc. as they can't feed on eggs.It would definitely need to be treated like a quarantine situation and get them away from each other...
I wonder if you'd be able to separate them long enough to treat the female and then put them back together? But I imagine any residual treatment product would probably not be good for eggs though...
Kind of a poo poo situation...