I would guess that the tractor alternator is quite small, basically only sufficient to keep its starting battery up. Depending on the size of the tractor, it could be in the 15-30A range. (It also has little need of working very well at idle speed since a tractor is generally operated at full rated RPM.)
I second the suggestion of getting an inexpensive generator. Even one of the little two stroke 900W units would probably serve you okay for this situation; they should be able to power the converter to charge up your 12V batteries, though you might have to force the fridge to run on propane during that time.
If you're feeling rich, there are nice PTO-mounted and powered generators available for tractors that would do a fine job here, too, and might prove useful in other circumstances.
