Tough proposition !
I don't see anyway out of this under the circumstances (her living with you) short of "radical honesty" ! Get a book or two in advance from the recommended lists we have on here and be prepared to offer her some reading material to understand your choices.
Like you say - if it were only an occasional thing you might be able to work around it. But even that doesn't 'feel good' and can flavor the relationships. Probably best to get it out on the table - assuming YOU GUYS are really committed to poly living.