Call the doctor's offices directly and ask to speak with their business manager. Have a frank dialogue about your situation and see if they can speak with your insurance carrier. Considering your daughter's situation, they were likely considered "emergency" procedures and many practitioners were likely out-of-network.
When my son was born, I received a bill from the NICU pediatrician who was out-of-network and called in for my emergency C-section. I called the doctor's office and they called my insurance company. In the end, I paid the bill and the insurance reimbursed me. My mother had spinal surgery several months ago by an out-of-network doctor and was able to negotiate the bill down by almost half by offering to pay in cash the amount owed to the physician.
As each bill comes in, start calling the doctor and the insurance company. Document when you called, who spoke to and what they suggested. Make sure to follow-up with letters indicating the bulk of the agreement.
If all else fails, most doctors will allow you to go on a payment plan that will stretch the payments out, with interest, into managemable chunks.