What size battery bank did you have to go with for the house batteries? That's the part I'm having a hard time getting a clear answer for. I only want to use the alternator and house batteries while driving. Not while engine off.
There isn't a clear answer to that question other than "MORE".
The basic size of a battery or bank can be measured in Amp-Hours (Ah); this is a number that should be on the label of basically all batteries these days. Essentially, it tells you how much juice (in amps) a battery should be able to provide for 1 hour (under ideal conditions) before becoming discharged (dead). Old batteries will probably have less, and realistically you're never going to be perfectly charged up to 100%. Here's something from l'internatz that tells you more, better than I can:
https://battlebornbatteries.com/what-are-amps/ .
br> Essentially, when everything is off, all of your power is going to come from the house batteries; unless you've got a more complicated electrical system that automatically shuts-off the batteries whenever you're connected to shore power. Even so, without regular discharge cycles, you're likely to wind up with some "plating" in your batteries (depending on their chemistry) that will reduce their charge/max capacity. It's actually healthy for (most of) your batteries to let them actually do some work and power something and drain down halfway regularly. Even the superior Li-Ion chemistries like LiFePO4 benefit from a bit of a regular stretch.
Your alternator is attached to the engine to take (spinny) power from it and to push electricity into your "truck" batteries. There shouldn't be a cross-connection from your truck batteries to your house batteries without some kind of isolation circuit, such as a smart-isolator or some kind of DC-DC charger; particularly if you're using different battery chemistries, different battery sizes/form-factors, or you have alternate power sources such as solar. Without some method of charging your house batteries, they're just a big, heavy, expensive brick(s).
How big your house battery bank needs to be depends on what you want to use it for, and how long you'll need to use it before you can charge it up again. If your usage is something like a simple 12V fan and a light or two like in a Mack truck or something, you should be easily able to get by with just about any-old automotive-sized RV/marine battery. If you're looking to power an 800-Watt window A/C unit, a hot plate, all of your internal lights, and some other fancy doodads, then you'll need a lot more than any single battery can provide. Probably something like four 8D-sized batteries at a minimum. If you need all that to be powered overnight before the solar kicks on again in the morning, then I'd seriously consider eight.
If you have the chance of being caught in a week-long rainstorm, then I would seriously consider figuring out some way to charge them up, because that's too much battery to reasonably fit someplace without giving up something like water tank space and weight.