My income is 16x the monthly rent yet the screening process and rules were very stringent (or so I thought) to include no pets or roommates.

They have 2 cats that they swear use littler box and they are willing to put down pet deposit and monthly pet fee.  

Forbid couples to live in rooms rented to singles and put in a $500 non refundable fee for unauthorized or even visiting pets.

My wife and I decided to raise requested rent on both sides of the duplex to $1025 and $1125 per month (plus $25 pet rent, based on experience with pets so far) and still generated plenty of interest.

I’m considering placing Section-8 tenants as well and was wondering how the security deposit or additional pet/service fees are handled- tenant or agency?

Pets are included in my lease. 

The other is a professional couple relocating from out of state. 3 young kids.In your experience (especially with responsible higher-end tenants like these) which is a greater risk for damage, kids or pets?

Look at creative ways to raise the rent, pet rent, lower deposit, etc... rents are superior to deposits because you never have to return them +/-Does this help?

I have a client relocating to Charlotte area (preferably Concord) and needs a short term rental that allows pets and prefers a fenced yard under $1,200 p/month. 

There are ways to off set the fee, charge pet rent (I charge $250 non-refundable and $50/month per pet), some tenants have two dogs and pay $100 a month extra.