Edit: Hopefully, "at home" would then mean "at the daycare", otherwise it's a bit irresponsible...
In another post I bring up the excellent point that the proper solution to the 11 hours in the office problem isn't making the 11 hours more bearable by Fing off for several hours per day, but perhaps only spending 8 hours in the office per day. Or less.
My wife did half days at home for almost a decade while the kids were little. They trusted her to work at home during an emergency at 3am, so leaving work in the afternoon to pick up the kids at school then working at home from 3pm till 6 or whatever was no big stretch of the imagination, even for "big corp" "dilbertian" management. This is obviously only applicable to cubie/desk jobs not manual labor.