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.

Or, let's say the housing office determines there is an extra adult living there, and you should have known about it.

Tenants in higher priced property will be responsible adults with jobs and they will have some level of education. 

The seller is an adult & can counteroffer if it’s such an insulting offer.Also, are you using the seller’s agent to write your offer?

There were young people at the games I attended (at a private home) and it was interesting to watch how a ten year old approached the business differently than the adults. 

Later, when you’re an adult you can decide if you want to go to college.

Part of adulting is making choices like this that include sacrifices that lead us ultimately to a better life.

The woman had initially contacted me and stated there would be two adults living in the unit.The woman texted me back a few days ago and referred to the man as her boss (not boyfriend or husband or anything).

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.