@Tamika Davis One of the biggest advantages of most software on the market is to complete these tasks you mention (maintenance, leases, rent collection, etc). 

Nathan above gave some good software recommendations, any of which would probably work well.

There software can tract really small differences in what's presented and what it should be.

@Julie Doke: Industry specific software speaks to you and you can easily relate it to your day to day process.

So accepting and approving multiple applicants is the norm?

I'm wondering if there's a software out there that could connect 2 separate VRBO accounts to resolve this issue.

We use a loan servicing software that has a monthly subscription. 

Are you not necessarily denying him based on screening criteria - Some landlords make it a requirement to view the property prior to letting the applicant apply.

The only example I can think of is that I asked an applicant questions about their credit report.

Quote from @Ryan Konen: You are correct that comping software like Privy, Propwire, and Propstream primarily rely on public records for their data, such as county assessor records, MLS feeds, and sometimes 3rd party aggregators.