Induction help

Hi ladies… I’m in a weird situation bc of my insurance. My insurance changed first of the year slightly and I’ve just been told my current obgyn office/hospital are out of network…. :( they didn’t realize until now and I’m 34 weeks pregnant I’ve had some complications (thyroid and GD) I want to stay with my current doctor I’ve seen for 2 pregnancies now and pay out of pocket until I deliver then deliver at the hospital I’m in network with. They are saying I’ll have to be induced at 39 weeks. My question is did anyone get induced/deliver at a hospital your doctor isn’t affiliated with? Let me know any knowledge/information you may have! Please and thank you!