Uh...nothing should be at 2v.
An alternator has a sort of "clutch". It's not mechanical, it's a magnetic field. The voltage regulator turns that field on and off, and that is what causes the alternator to make power or not.
When the alternator is spinning it supplies its own power to "energize the field coil". But when you first turn on the key, and the engine is not running, power has to be supplied from the battery to energize the field coil.
The wire from the battery that feeds the field coil, is ignition switched and usually runs though a light bulb. That is the red alternator warning light on the dash. If the alternator is making power after the engine is started, then no power is being pulled though that light bulb, and the light is not lit.
Your solenoid was connected at the blue circle, and it sounds like they moved the connection to the yellow circle.
Which is fine and should work, but the voltage at the small terminal of the solenoid should be the same as the engine battery voltage with the key on but the engine off [EDIT: actually, sorry, the same or perhaps a bit lower after going through the light bulb), and should be the same (or a bit higher) than the battery with the engine running. (And should of course, be 0v when the key is off.)
Sounds like they probably tapped the right circuit, but likely just got a crappy connection somehow. I doubt that 2v is enough to pull the electromagnet in the solenoid and tie the large terminals together, in which case, the house battery would not be getting tied in, and not getting a charge.