Assorted thoughts, some (OK, many) in reaction to comments above this one.
WOHM to a kindergartener here. From 2m to 3y DS was in paid care part-time, with grandparents part-time, and with parents (one or both) part-time. At 3, his dad (my DH) retired. The care situation really didn't change except that DH took on a bit more and I took on a bit less. The year DS turned 4 we went to more paid care and less grandparent care. DS is now in public kindergarten.
I cannot begin to describe how valuable the paid care we have made use of has been to us. We are fortunate to live in an area where we have had access to a number of good paid care institutions/setups (we've used two in-home and one "institutional" settings). Though others (above) claim it is straightforward to find opportunities to interact with other kids and this might be true for many parents, in our community (many 2WOHPs) and given our personalities (not that keen on playdates, playgroups) etc. we have not found this to be true. And of course having just the 1 kid (not by choice) we do not provide that (inherently) in the home, either. Giving my kid access to a fairly stable "playgroup" (well, really several different ones over the years) has been one of the best benefits of every care/school setting he's been in so far up to and including kindergarten. Our experience in this regard has been very different from @KDMS's, so obviously YMMV depending on the daycare options available to you -- but it sounds (?) like you have a setup you are already happy with?
Our use of paid (and now public) schooling notwithstanding, I'd challenge anyone who says that we're not our son's primary caregivers. We are, of course, engaged with the care provision and providers, as well as with our son himself. But Alandjackson's experience that using paid care results in the kids spending 80% of their free time in someone else's care doesn't jibe with mine; my son sleeps about 10 hours/day (if I'm lucky!), so doing the math and ignoring those hours, 8 hours 5 days/week in daycare (we've never actually used that much, but taking it as "typical," and assuming no holidays/family vacations/sick days) would provide us with on average a paltry 8.25 hours/day (on average; less on the 5 days/week he'd be in daycare, of course) to interact with him. Bluntly, this is more time than I personally want to interact with a preschooler/kindergartner, so using care-provided-by-others has not left me feeling I don't get enough time with my son. There are, of course, moments of "lumpiness" -- DS and I are usually together too much time on Saturdays, when dad plays golf, and not enough on one or two weekdays each week, when I work late or opt to go out in an evening for some "me" time (or DH and I go out for a, gasp, date). But we muddle along and do just fine on average.
I often see folks advocating "[someone, usually mom] staying home while the kids are small," and while that's great if it's what you want to do (and can attain; sadly, it's not an option for everyone who wants to do it), it often seems to me to be counterbalanced by the idea (rarely explicitly stated) that you can "return to your career once the kids are in school." My take on that implicit proposition is that it's a gross oversimplification; speaking as someone who's had teenaged stepkids (as well as now a LO), kids do not cease to need supervision, care, attention during daytime ("workday") hours as they get older, and unlike LOs, good quality paid care isn't readily available (again, as it is in our area, YMMV). I'd much rather balance some work and some play over my kids' childhood/lifetime than front-load it (and honestly in my experience kids are much more devoted to the parents' perspective and guidance in the early years and much more eager to be shaped by outside forces in later ones, so, again, if the focus is on whose values kids are absorbing, I'd say there's reason to make sure you don't front-load the early years too much (which of course isn't making any argument at all against being a SAHP at any stage, including throughout your kids' entire childhoods. It's just saying that valuing having more time with your kids early versus late may not be as obvious a choice as it often seems to be presented as being.)).
OK. Off my soapbox. Mostly I'd just say to the OP (as many others have) that the finances don't make the case that either you or your wife should stay home to avoid/reduce daycare costs, so you should talk about what you want in terms of balancing time-for-work and time-with-kids and find a way to achieve that. My family has had good luck using part-time care (our first setup was 2 8/hour days week; the second was 4 4/hour days, and the third a blend of 2 4/hour days at the same 4-hour place and 2 8/hour days at another), but it's harder to find (around us anyway) than full-time setups, and we have paid a premium (seen as a per-hour or per-day rate) relative to purchasing full-time care. Plus I wouldn't advocate the half-day thing as time-efficient because honestly by the time you drop the kid off and pick up, best case you are down to 3.5 hours of no-kid time, which just is hardly enough time to shower (kidding, kidding!) (however, if you can arrange for one of you to drop off and the other to pick up and have flexible work schedules, this could be a great option). With two kids, you'll likely want to prioritize finding a place they can both go, and be dropped off/picked up at the same time, so that's something to factor in that may constrain your choices.
GL finding an arrangement that works for you.