I agree with looking at it as a one-year-at-a-time proposition, especially at this point. So, looking at next year:
Your concerns with school are the negative socialization, the stress and the lack of meaningful learning. If you try private school for a year you'll find out whether those issues are solved. If they're not that means extending to two full years, for very young children, the problems you're currently seeing.
Her concerns with homeschooling are missing out on parties, holiday celebrations and the culture of school. If you try homeschooling for a year, you'll find out whether missing out on those school trappings is a problem for your girls. If it is a major problem, that means your girls will miss some fun school events during 1st grade.
Which is the most serious risk? Missing a year's worth of school parties and special events, or enduring a year of stress, negative socialization and lack of meaningful learning?
To my mind, from what you've written, it's no contest. The year of homeschooling wins hands-down. And yes, what you're feeling is very common. Anytime you plant your feet firmly outside the flow of mainstream culture there's bound to be some self-doubt that creeps in. But think about it: because something feels instinctively right is no reason not to trust your reasoning that it's right. If your heart and your mind were saying opposite things, that would be cause for some careful reconsideration. But in this case, they're in accordance.
Mountain mama to two great kids and two great grown-ups
Just in the past month we've attended: a kid-made craft fair & recital, winter dance, talent show, skating party, medieval weapon making workshop and winter holiday legend/storytelling party. And this is just what we chose to attend during our "slow season"; not even a fraction of what was on offer!