What should I do to prevent mold from flooding?
What you describe requires major plumbing work and can cause devastating damage to your home.  Your landlord should be responsible for fixing this because with moisture leaking behind the walls like this then it can quickly create major property damage to his rental unit and unhealthy mold.

Your landlords refusal to fix this on his own is creating a health hazard for you, and in many countries and states there are laws that protect tenants and give them certain rights in a landlord-tenant relationship.  One of these rights is the right to a safe and hazard free home, which means you can and should be able to bring suit against the landlord in the event where he refuses to fix a situation with the property that is creating a signficant health hazard for you and your family.

To get rid of the mildew, talk to your landlord and tell him to fix the leak immediately.