R.W.
If they are really interested in having you for the newer job maybe you can make some kind of bargain for getting a flexible schedule?
What about longer days MWF and shorter days (or differently scheduled days T TH?
I used to work until about 3 or 4 PM and I still felt like I had no time with my kids, because when I got home it was forcing them to do homework, then it was cooking, eating, dishes, laundry, showers, bedtime.
Basically I nagged at them from the time I got home, til bedtime, just to get everything done...it sucked.
There have to be more choices than the two you see now...I would try to make a deal about the schedule, or try looking for a different job that has a more workable schedule. How about something that is stimulating but part time?