If we agree to both take a few days at a time every couple weeks and leave the other with the kids in the house, is that a bad thing? Isn't space what I should be providing right now?
I would talk to both your family law attorney (because there may be legal implications for anything you do or DON'T do in this regard now, moving forward) and also a good family therapist. I'm not either, but what you're describing could be very confusing to your kids unless it's handled properly. Their emotional well-being and feeling of safety and security need to be your #1 (and #2, and #3, and . . . ) priority right now.