Windstar 2002 3.8L Limited - Engine cuts off while driving.?

The car was running fine until I replaced the alternator with a re manufactured alternator because it was cheaper. Kent Easthill Tire put a tester on the battery and said the alternator was not charging properly so I took their word for it and replaced it. Now the car will start fine and idle forever but as soon as you take it on the road without warning the engine will quit whether at 10 mph or 60 mph or accelerating. While the engine is running it runs fine without missing or anything. On the road when it stalls I have to turn the key off first and then it will start right away. It has good power and then without warning the engine quits. Anyone have any thoughts to what would be causing this? The car is sitting at the dealership as everyone is scratching their heads as to why this is happening.