It is a common misconception that the power you get from the alternator comes for free. IT DOES NOT.
It takes GASOLINE to run the alternator - with the resultant 20% efficiency of the gasoline engine, and another loss in the alternator output.
The electricity splits the water into oxygen and hydrogen with yet another loss of efficiency.
The oxygen and hydrogen are recombined in the internal combustion engine, along with the burning of gasoline and oxygen. This is a further loss of efficiency.
Adding oxygen and hydrogen to the input gas stream DOES NOT improve the efficiency of the gasoline burn, and CAN NOT produce more energy than is put in.
Throw a solar panel on the roof and use THAT to crack the water, but do not think you will get any improved efficiency from cracking the water with the alternator.
You have thrown your money away if you think this will work. The law of conservation of energy will beat you every time. It's the same as trying to make your car levitate - the law of gravity is your enemy on that one.
I look forward to seeing how you convince yourself that this is working, but I predict that you will be rather disappointed.
Here's a link for a bit more information on hydrogen.
http://www.tinaja.com/h2gas01.asp