I have only one child, and she has never attended a conventional school.
From the time she was four, we allowed her to do educational activities (informally, sort of a Montessori-but-not-really at home approach).
We switched to more formal instructional materials (workbooks, Reader Rabbit computer games, and Singapore math in addition to library books... HUNDREDS of library books) when she was five, and by the time she was six, she was working at about 3rd grade level and accelerating.
We enrolled her in a virtual charter school at that point since we were concerned about her ability to work on weaknesses like writing, and her asynchrony was worsening with eclectic, child-led homeschooling.
She has been with the virtual school for the past six years, and is now (at 13) a rising high school junior.
I worked at least 12-20 hours a week as a research faculty member during the period when DD was three until she was ten.
There were a series of factors associated with the decision to have me leave my job; soft $ funding, which ran out and we opted not to renew, my DH's employer increasing output demands upon reducing global workforce, and DD's increasing need for more hours from a parent.
For us personally, it has never worked very well to have Dh do 'school' with DD. She doesn't take him seriously and resents the intrusion of schoolwork (which she often regards with significant disdain) into the Daddy-Daughter let-the-good-times-roll dynamic that they've established from day one. (Yes, this would make me "Bad Cop.") As asynchrony peaked during middle school (organizational demands, work output increases, especially written, and increased cognitive ability in a PG child meaning increasing boredom with school and impatience/intolerance for developing study skills and academic weaknesses) and paired off with nacsent adolescence into a toxic brew, it was really important to have a parent on-duty all the time. The same parent, actually-- DD is quite manipulative.
As I said before, though, if we'd had a nanny (as we did when DD was a baby, when DH and I were both tenure-track faculty) it could have worked indefinitely with sufficiently flexible employers.
HTH.
