Insurance: OB gyn covered, not the hospital

I just found out that while my Ob gyn is covered under my insurance policy, the hospital where she delivers is not in network 🙄 So if I delivered at that hospital it wouldn't be covered under my insurance. Apparently this is one of the ways insurance companies can "trap you"... but there's hope! Apparently my OB gyn can pre-certify the hospital at her discretion and the process would take 7-10 business days. If that doesn't work, I'll either have to get a new OB gyn or new insurance...? My insurance also doesn't cover home births. I'm looking into it to see if it covers certain birthing centers... Maybe I can do all my pre-natal checkups with my OB gyn and then just deliver at home?