Terrible idea to start a transaction with tax fraud!

If the background check is screwy you can hand her information over to authorities and you now have an address to send your letter for a $30 reimbursement or threaten her with mail fraud and hand all her info to the United States Postal Inspector and Alaska State Police.

Keeping communications and bookings on VRBO helps to protect you and travelers from phishing and other fraud.• Auto-declines hidden from search results: If a booking request for one of your properties is auto-declined because a traveler has not received a response in 24 hours, we may proactively hide the property from search results to help preserve your search ranking.

If the two units are identical you could split those expenses in half. 

Just be very careful you aren't committing Mortgage Fraud.

Randomize the order, find some accepted cultural markers for coffee table books and decorations to switch out (when academics have done "resume research," they use names that are 90% one group or the other -- "Jake Smith" is generally a white dude, "Jamar Smith" is generally a black dude, so when Jake gets 50% more callbacks with an identical resume, there's good reason to suspect foul play). 

Check credit, criminal history, eviction history and verify identity and then income with the employer. 

They had identical floor plans. 

The payment process for you is identical to paying a regular mortgage except it goes to a different 'Pay To' address.

I would make separate sites and have a link to each other's site which will help with SEO and also give each it's own identity.