Well, to answer your last question first, the voltage regulator - or in the case of modern cars, the engine computer - monitors the engine's battery's voltage and cuts the alternator output back to prevent overcharging the engine battery.
As far as sending 130 amps to the house battery, remember that the principle function of the alternator is to run the engine and accessories. Ignition system, electric fuel pump, heater/ac blower motor, headlights, windshield wiper motor, etc., etc. etc.
The only current your house battery will see is what's left over after all of those things take their share.
I would guess that at night, in a storm, with the headlights, heater, and wipers all running at once, there wouldn't be a lot left over for the house battery.
The other factor is the size of the wire you run back to the house battery. The fatter the wire, the more power will flow.
Most people here just pick a 100 amp continuous duty solenoid and call it good. I'm sure considerably less than 100 amps will flow through it. Exactly how much is something you'll have to determine by measuring it with an ammeter while it's running.