charging battery directly from a source, what could go wrong?
Okay,  lots of stuff to talk about.

The thing about battery charging is that the battery has its own voltage, so resistance is only half of the story. If the charger is at 12 volts, and the battery is at 11.6, then the .4 volts difference is all that is pushing the current into the battery. This small voltage divided by whatever resistance it finds in the cables and battery determines that current. You might see a 100 amp peak, say when starting an actual car. That causes a rather large voltage transient.

And then, that isn't exactly right either. The voltages that you see while charging will be really very close to each other, and what's actually happening is you are replacing electrons in the battery chemistry to make its reaction go backwards. Its just a lot easier to model this mathematically as an ideal voltage source behind some internal resistance.

But the resistance is a real thing. Professional tools actually place a small value of AC current through the cell and take an AC voltage reading across the cell. This and Ohm's law gets you the value of the internal resistance for the pack or cell, wherever you can get terminals to check it. But, generally, this won't matter to you.

Hooking it all up together will work, with the caveat that diode Vladimir mentions needs to be in the line so the battery doesn't discharge through it. It may be built into the alternator already, maybe not. Do check that. What will happen is that when the battery voltage and the alternator voltage are the same, with no other loads connected, no current will flow.