In-network hospital system won’t submit claim

My child saw an in-network provider at an in-network hospital system. I provided the insurance info at the time of the appointment and the provider sent a claim to the insurance, it was accepted, and I paid the balance. I later received a bill from the hospital system for the same appointment that was not itemized – just the DOS and an amount owed. It indicated insurance had not been billed. I used their online portal to provide the information, and was sent a second bill. I used the portal again, and received another bill. I called the customer service line and provided the insurance information and they sent the account to collections. I’ve now filed a dispute with the collections agency. I double checked with the insurance and the hospital system has not filed a claim for that DOS, just the provider. Now collections kicked it back to the hospital and I’m waiting for the hospital system to file with my insurance, and maybe they will call me, maybe they won’t.

I’d rather deal with this proactively than wait, since the hospital system has proven repeatedly they won’t submit the claim to insurance. I filed a grievance with my insurance company. Is there anything I should request from the hospital system or send to them for documentation purposes? Can they refuse to submit a claim to my insurance if they are in-network? Anyone dealt with anything like this and have any tips? Thanks in advance.