I refused to let her have it since I have a no pet policy and she threatened to break her lease.

Second, code enforcement gives me 3 days to correct life threatening situations.

I told him no i can't pay for it. but he is insisting that i do it and is threatening to move. what's the best way of dealing with it?

I've threatened eviction before, even filed the documents and had a court date, but have never made it to the hearing before now.  

He even threatened to report the company to the Labor Board. 

But if they fail to adequately screen them and rent to one who robs or hurts a neighbor, they could be sued by the victim for negligence.No doubt many will see no option but to raise rents to indirectly exclude criminals from their rentals, which will just end up hurting everybody who rents housing — including innocent, law-abiding tenants.Obama’s new rule makes it easier for HUD to resettle urban minorities into affordable housing in the suburbs, as part of a controversial regulation it finalized last year — Affirmatively Furthering Fair Housing — which threatens to cut off funding to local municipalities that refuse to lift zoning restrictions on low-income housing.The federal mandate — whose goal is racially balancing the nation, ZIP code by ZIP code — also threatens to import violent crime into the suburbs, while lowering property values and negatively impacting local schools.As kitchen table issues go, these are major developments.

Once a tenant (unfairly) threatens rent, your relationship with them is over.

They refused to call a real heating/a/c company, until I threatened to report them for providing inhabitable housing due to lack of heat. 

All I can advise you to do is threaten to sue them if they don't let you out of the contract. 

He only responds to me if I threaten to take expenses off of the rent.