I'll preface by saying that we don't have kids. In our early/mid 30's my wife's career started to really take off. Both engineers making a good living, but it didn't take too long for her to start making 2x what I did, then 5x, then 10x, and now beyond that in our 40's. My salary became little more than a rounding error and working my job was no longer worth the stress, hours, and travel to either of us, so I quit. Sitting around the house taking care of everything for our massive 2 person household didn't feel right either, especially to people on the outside who liked to voice their opinion on the matter. I ended up going to grad school and getting a degree in something that I thought I would find more interesting. Upon graduating and getting a new job in a new field, I immediately figured out that when you're FI, a job is a job is a job. I've completely lost motivation to work, but don't just want to sit around the house while my wife works either. We're FI now, but the wife wants to continue to work as she loves her career. My compromise to myself was to work a lower level analyst type position until she decides she's had enough, which hopefully will be in our late 40's. I work 40 hours a week, have no work phone, laptop, access to email, etc....I go in, do my job while trying not to think about it and put it out of my mind as soon as I walk out the door. My employer is actually thrilled with the situation since they're getting a highly educated, skilled, and experienced person to fill a role that would normally be filled with a younger, level 2 type recent graduate. Boss just knows that he can't call me after hours or on the weekends. It's a good fit for both of us and after a couple of years, seems to be the best thing I've been able to put together.
Having said all that, if I were in your exact shoes, I'd try and dial back the fancy lifestyle a bit and try the SAH thing. If you don't like it or it doesn't work, you can always go back to work. It could turn out to be the best thing you've ever done for yourself and/or your kids, or not, but it sounds like the PERFECT time to at least give it a try and see what it's all about. I wish I would've had a parent around as a child, mine were always at work.