Landlord refuses to fix broken pipes and leaking roof on rental property

From your description, it sounds as if you have been constructively evicted. That’s when the condition of the premises is such that you can’t make the use of what you’re paying for—in this case, living there with your family—and you are essentially forced it. The concept is similar to the ideas of the covenant of quiet enjoyment and the implied warranty of habitability, which pretty much mean what they sound like: you have a right to enjoy, or use, the place you’ve rented, and the place must be habitable.

When you’ve been constructively evicted, that can serve as a justification to break the lease; or more properly, it’s the landlord who’s already breached the lease, by forcing you out. The constructive eviction therefore lets you out of the lease. It’s also a defense to the landlord’s demand for rent—you don’t have to pay if can’t live there.

Furthermore, you could even sue the landlord—damages are available for constructive eviction damages. As in any other contract case (a lease is a contract, after all), you can sue for (1) anything you’ve already paid, while not getting what you paid for (i.e. any rent you’ve paid while the place is uninhabitable) ; and (2) additional costs you’ve incurred owing to the landlord’s breach, such as costs to move, to store belongings, or if you have to rent a more expensive place, the difference in rent.

Important! If you claim to be constructively evicted, you have to act now—move, bring a legal action, etc. If you simply remain in the place, you weaken your case, possibly terminally: after all, how could the conditions be so bad if you’re staying there?