The cost in flooring damage alone from their animal dictates it.Although, it sounds like it's resolved now - good job!

So, you need to see what laws dictate what you can do.If your lease says you can evict if they don't pay their fees - or the fees are written in such a way that it's part of the lease agreement, and then you can call it a breach of the agreement - then yes, you can evict for non-payment of fees.So, step 1 is to figure out what laws govern your situation.  

Markets dictate pricing. 

Assuming the rental is in seattle as OP is,   Seattle has an (annoying but its the law)  ordinance https://www.seattle.gov/civilrights/civil-rights/fair-housing/first-in-time dictating how rental applications must be processed -  This is the first-in-time ordinance.   

The market dictates pricing so simply check to see what comparable properties to yours are currently renting at and then notify your tenants that the rent will be $x beginning on (date) and a new lease will be needed. 

How in the world can they claim there is mold then dictate when and how it will be remediated while you provide alternative rooming... and now they want A-Z... consult an attorney and get out of this situation ASAP.

I've let tenants dictate terms too much and that stops now.I've had to learn my lessons the hard way in this business.

That would also dictate what you need to do.

The bigger point is allowing the tenant to dictate improvements on your property.

The other tenant (a new tenant) will have a lease that dictates they pay 1/8 of the water bill.