Hey there - Have you though about using a birth center? Not quite a homebirth but a lot less intervention than with a private hospital.
I understand where you are coming from. I'm also private and decided this due to a very compliacted 1st birth experience (prem birth at 28.6 weeks, placenta previa and placental abruption). I am just not comfortable with a homebirth, but would have loved a birth centre ad a compromise (they wouldn't accept me due to the issues of my last birth).
My last birth was totally medical- and life saving- however I'm hoping this time for as un-interventionalist as I can get so have chosen an OB who is supposed to be good with VBACs and a Doula. I do, however, dread being pushed into things...that's why I have my Doula for extra backup, support and advice.
Goodluck hun. And don't feel stupid. We all do what we feel is best at the time we are making the decision. If you are going private, probably the best way to get what you want it to have a Doula too?