As a SAHM whose children are privately educated (but have had many go through the state system) I would like to say that I don't actually think that my children will get higher results - that's not why I sent them in the first place. However, I do believe that the experience the children have is, in general, 'better'. Not just a little better either, but significantly.
One of mine currently in a private senior says that she'd choose her current school any day, just for the sheer adventure that each day presents. She's in year 11 and has been attending since year 7. She was, incidentally very happy at her state primary school. My younger child is in prep school and is exceptionally happy. I can see having experienced both, the differences - in some areas are more subtle but in most it's vast.
This doesn't mean that I ever look down on or see state education as 'repellent' though. It just means it suits us. I've had my children attend lovely state schools in the past.
OP - I do understand your feelings though and I think YANBU. I can't see why others have taken exception to your post, telling you to work. I see that if you worked you'd rue not staying at home. I understand your feelings though totally, you're very happy being SAHM but you can't help feeling jealous of those who have children privately educated.
YANBU IMO.
For what it's worth, if I had to choose, I think I'd choose the SAHM but then I'd home educate, definitely.
Could you consider that perhaps?