Health insurance provider refusing gap coverage for out-of-network provider [x-post /r/legaladvice]

Background: Daughter broke her jaw, went to in-network Emergency Department, was referred to out-of-network specialist for follow-up treatment (maxillofacial surgeon). Insurance gave me name of an in-network specialist, however, in-network specialist is refusing treatment because “they don’t take patients from that ED” and refuse to take patients “from their only competitor.”

Due to their refusal, at this point, my health insurance cannot provide me with an in-network physician to handle this issue. They are denying gap coverage for an out-of-network because they require an in-network physician to fill out the form to apply for gap coverage. My daughter has not seen an in-network physician in the past year, her primary doctor is a DPC clinic and they don’t take insurance.

What are my options here? My take is, their only in-network provider is refusing service because we went to the wrong ED, this isn’t my fault or my choice, I went to an in-network ED and don’t control who they have on-call for every specialization. If this injury turns into surgery it could rack up to tens of thousands of dollars really quickly. Location is Kansas, if that makes any difference.