My two "adult" children currently live there but they will be exiting the property in January.  

Even adult children who the parents want to be occupants not tenants on the lease.

I tell them I need an application filled out by each adult.  

That's what I do.My lease specifies where tenants can park per city/neighborhood rules.One adult could have one car and 10 kids... occupancy and cars need limits on each (assuming your area allows occupancy limits on humans in bedrooms).If your tenant has too many cars, does your neighborhood fine your property... or put a ticket or tow the car itself?

I am very new to flipping houses, however I have been in construction and remolding most my adult life.Currently I have three houses on the market, from my calculation and with my real estate agents help I priced them at what i think is just below market value.

Are these three unrelated adults?

I require all adults to be screened and on the lease.

I learned she had her adult son living with her.

Many landlords force all adults to be tenants, but that can create headaches if things sour between them.

Are you saying that I should run credit checks on all perspective adult tenants.