They also say the family would do all of the signing of lease, the background checks, application, etc.

Unfortunately, the only time you have the ability to really determine who is there is during the application process.  

Always run a full credit report on any applicant.

I keep marketing the property and accepting applications until someone completes the entire application process.The first couple who applied with us this past Friday has paid their application fee, had background check ran, and submitted ID, but still hasn't provided two months past pay stubs because they recently moved from out of state.Now another couple views the property today and completes the entire application process outside of signing the actual lease and paying the first month and security deposit.My thinking is I'll take all applications until the first qualified tenant completes the entire application process.

Often there are leases, applications, pet agreements, and dozens more forms that you can buy and use through the apartment association that are drafted specifically for your state laws. 

I am trying to add my mom as co-applicant; she is on the title and mortgage as well, but she lives in a different state and has her own primary residence.

The problem with that is I'm only recently finding out that there was a special cash out window when I left the company, which would've made me indeed eligible for a lump sum distribution, whereas I would've been able to commence a full unreduced rollover.The administrator is now Xerox, who claims they have no record of receiving an application for benefits from me based on the information provided by Hewitt once they relinquished administrator, nor do they have a way to verify what was or wasn't handled properly by Hewitt.

The applicant is the only person that can request the investigation.

We are more apt to accept a borderline applicant than keep the unit empty for longer than a week, and we pay the consequences of that.  

After a few days more questions started to arise; the woman was going to have her dad move in at some point, they were going to be gone for some months, and they wanted to send payments from an account in Italy.They were also adamant about not providing social security numbers on the application.