With my insurance BCBS of Or here's what happened both times:
Dr/mw had a set fee for prenatal services and delivery (say $4000). Dr office contacted ins co to find out my benefits/deductible/copayment. The ins co expected that they would pay $3000 of the dr fee. Then the dr/mw told me I owed $1000 to them. They wanted me to pay $1000 prior to birth and wanted to set up payment plan.
When all the bills went thru (1st birth) the dr bill went thru after we had maxed out our yearly amount owed and we were refunded our cash payment.
Op- get a copy of your dad's ins card (or his plan info #) and call the ins co yourself ask to speak to cs rep and have them explain what your maternity benefits are. You shouldn't need your dad to talk to them. This should clarify if the dr office is billing you correctly.