@wasblindbutnowisee It sounds like you might have to rethink your entire family arrangement.
Maybe there is a way for you to do less hours, and for her to do a small job for a couple hours a week? That way she gets to have a sense of accomplishment outside of the home, and due to the extra income you could cut back a few hours which should leave you less exhausted.
Also: Childcare is work. Household chores are work. She needs breaks. And not "I'll do the laundry while you watch the kids", she needs an actual break, where she has no responsibilities. Because even "just" watching the kids IS WORK. That's why babysitters and kindergarten teachers aren't volunteers, it's a job that gets paid.
Imagine how many people you would have to employ to replace the work your wife is doing. You would need a maid, a cook, a babysitter, a secretary, a personal shopper. Your wife is doing the work of 5 people, round the clock, with no break. She is always on call. Of course, you are exhausted after your 12 hour shift, that's absolutely understandable. But she is too, she also lived through the same 12 hours and right now, her shift never ends. Maybe this will open your eyes.
SUGGESTION:
Person one goes to work, person two takes care of kids and house. As soon as person one comes home, person twos shift as stay at home parent ends, too. Now both are responsible for everything in the house equally. Person twos next shift as stay at home parent starts as soon as person one leaves for work.
This is what friends of mine do, and this is what my partner and I plan to do. We also both plan to work part-time, so we take turns being the stay at home parent.