What would cause the floor in the front and rear of our car to flood?

Unless it's something extraordinary, a leak in the heater core is about all that could cause it. It may be that condensate from the AC core is draining inside the cab, but that is unlikely. If it's a heater core leak, the fluid on the floor will be engine coolant, and if you have anti-freeze in it, you'll have that on the floor. And your engine coolant level will be dropping. It is possible that the engine may be overheating for lack of coolant.