Yes, your family plan's account owner would be responsible for paying any ETF if you port your number to another carrier. You would need their permission to port the number anyway if you are not account manager on the family plan account. I would suggest finding out when your contract is completed on the family plan and port your number at that time.
In the meantime, you could consider getting a prepaid phone with a new number from Verizon to find out how well the service work in your location to compare to Sprint. Then you can have the calls from the Sprint phone forwarded to the Verizon phone.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.