The independent school thing is a red herring, so I will ignore that.
SAH or WOH - I don't know why people get so upset over this debate.
First, you don't have to choose one path when you are pregnant with your first and stick to it until the youngest leaves school.
I have been a WOHM to babies, SAHM for several years with more babies and primary aged kids, and now WOHM with all school-aged kids. Each phase has been right for me (and the rest of the family at the time). Each phase was a carefully made choice. I loved being a SAHM but after several years, I was becoming less and less productive. It was time to return to work.
I am fortunate enough to have a job where I can take my younger children to and from school, watch their matches, concerts and (although I decline) their assemblies. I can work flexibly in the holidays, so can be at home for as long as I want, especially with teenagers to fill in on babysitting. So, I earn about one-third of my BK colleagues, but there you are - I am content.
I am sure if you took a straw poll of Mumsnetters, you would find content SAHMs, content WOHMs, SAHMs who would like to work but can't afford the childcare or loss of benefits, and WOHMs who would dearly love to give up but who are significant breadwinners. You get everyone, but I would like to encourage anyone who is not happy at this time with their situation that it doesn't have to be permanent.