I knew I could easily find tenants/roommates as the area is popular for young adults.

No dogs allowed on a chain and only on a leash with adult supervision.  

The city that we live in needs something new, something big, something to bring the family's all together along with providing motivation for teens and young adults to get out and be active.

I have no problem enforcing our lease and threatening/going through with eviction, however I'm curious how I would prove that she has additional adults living with her.

In my real Estate brokerages I have owned 90% women  in lending lots of women loan officers and of course support staff is mainly women.. at The title companies I work with their is maybe one male and 10 to 20 females all the senior escrow officers are women.the only time i see men in the escrow side of things is back east in states that use attorneys to close deals and those are generally all men.. as in the attorney that owns the practice is male and his staff is generally female  Not all but majority of the companies I have closed with back east are like this,

At some point she will get tired of her adult son taking advantage of her and you will be stuck.

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For example, I mention that every adult must pay a $30 application fee, pass my credit/criminal background, make a combined income of 3x the rent, and whether or not the property accepts pets.

I explained I still needed all adults over 18 to fill out the application and sign the lease, because there is a criminal check involved also, but it was fine if only one person made the income requirements. 

Coping with the loss of her passing, I wondered , what had made her hold her head high and never ask anyone for monetary help even after we were adults and earning well.