A lot of the result depends upon how much energy your wife has to devote to homeschooling, after childcare and housekeeping. Unless she is above median/average, the answer is usually "not much energy". From the way you wrote, it sounds like you leave the house to work. Even if that is not the case, our field is competitive enough that even an easy "lifestyle business" will see you devote half a day every three days at a minimum to your work, making it challenging for both parents to be heavily involved. If you work at home, like most around here (including myself) you probably work a full 40-50 hours per week if not much more. The erratic nature of much at-home working also wreaks havoc upon the routine many young children crave to establish the level of trust they require; there is some clinical evidence that the successful children in the Stanford marshmallow experiment were successful because they trusted parents, which translated into trusting adults, and hence trusted the adult who told them they would get an additional treat in the future). So really homeschooling on a practical, continuing basis comes down on the shoulders of one of the stay-at-home parents (or the one stay-at-home parent).

I can tell you what worked for me, and leave it up to you to collect sufficient data samples to judge your own situation. We bring in a nanny 12 hours a week, on three separate days (8 of those hours are with a nanny who speaks a second language for an immersive experience for the children). My SO taught at home from pre-verbal stage to 4; we turned what most houses would be the "living room" into the school/playroom for the children.

Our local homeschool groups don't meet frequently enough to offset some of the lagging social development cues we suspected that were not aligning with our 4-yo's advanced verbal skills (assessed to at least a year ahead of peers), so we placed (for 15 hours per week) our 4-yo into a pre-school that specializes in Precision Learning and Direct Instruction methods (these terms are sometimes associated with developmentally delayed children, but they work even better with developmentally appropriate children). The rest of the time we continue with our homeschooling. Results: within six months, our 4-yo leapt from average to a year ahead in math and reading, and (our suspicions were correct) went from being uncomfortable in groups to being the class clown (never knew the child had that in them).

I will tell you straight up front: this is expensive. There is no way around that. Since you mention a state, I assume you are in the US. Using private resources means you will likely pay property taxes partly for a public school system you will not use. One decision we took to mitigate that was to hunt for a house that was only assessed county property taxes, and still as close-in to the metro area as we could manage. We gave up the amenities of urban living, but our city is not densifying and is growing rather dysfunctionally IMHO so I consider moving away a net positive for our particular situation.

Between the nannies, part-time pre-school, and third-party activities we signed up for that we don't have the equipment to teach (swimming and gymnastics), it is a significant chunk of change. However, I consider my children my most important investment, ever, and my capital allocation reflects that. As the children grow older, we do anticipate not having to spend quite so much on the nannies / housekeepers, so the situation does improve, but there are no easy answers here.