My question is this: if we have lived somewhere for over a year and are just now having what appears to be a mice infestation problem does our landlord have to commit to maintaining the vermin control with a company who wants a quarterly contract for the extermination or does the landlord only have to pay once and then the responsibility falls to us to maintain the service? Also if there are problems with the house, such as drywall or cabinetry that aren't up to code and are causing the rodents to nest here does that change what the landlord is responsible for? Can they say they aren't going to fix the problem and suggest we move?
No, they can't say that. They have to fix ALL the problems. Maintenance is the landlord's responsibility.