Not related to the power system directly, but I, too, operate a mobile office with a pooch. So far, the dog has been on five cross-continent trips, all of them boondocking. In 2019, we spent about 3 months living almost entirely off-grid in our van.
Husband and I designed and installed our own lithium system a few years ago. For the amount of work that goes into lithium, frankly I'd rather run the a/c off the generator if I can get away with making noise (e.g., stopped for lunch at a restaurant next to a freeway). We can run our roof a/c for about 2.5 hours on the lithium alone, but there are potential issues that are easier to manage if we don't have to (I'm omitting a LOT of detail for brevity).
I find that the secret to sanity is a large number of ergonomic mods and enhancements above and beyond the power supply. That includes a custom hitch carrier which we also made (my husband is a hobby welder), and a few other items you can see in this pic below, including a dog platform up front (less motion sickness on 6,000-mile jaunts - I swivel the seat around and have a custom cut plywood insert to span the footwell on that side), and this armrest table that I made to hold my snacks when I'm traveling thousands of miles solo. We've done a lot of other mods also, for space efficiency.