This is causing more wear and tear on what the house is made for, and the water bill im sure is going to be through the roof.

(water coming through ceiling) The owner says the tenant is required to do the maintenance.

"How you doing, your family member is selling me the roof over your head and you need to leave" doesn't seem like a good conversation starter.Lastly, is there an industry standard incentive that typically works to motivate "tenants" to move out sooner than later?

You'd still have the standard LLC protections but NOT from the lender as you are responsible for the payments. 

If a house is on a well then buy an water purification system, they are also available for purchase and installation. 

Sounds like a mix of not being the best deal, unvetted refinance rate expectations, and water leak are impacting your expected cash flow.

The tenant just put duct tape over it so no water could soak into the wood below and kept on using the countertop.

House took in 3-4 in of water.

I recently reviewed a list from a local township, and it looks like more than real estate taxes are considered with regard to tax liens (e.g. water/sewer, public utilities).  

You may be able to negotiate this into your management contract.Sewer / Water: $30-40/unit/month.