My daughter's father hasn't had any contact with us in over 3 years. I have tried multiple times reaching him directly or through his family, but he and his family refuse to get in touch with us. Is there any law that permits me to get his rights relinquished, permanently? Oh, we live in Indiana :)

Getting his rights totally relinquished can only happen if someone else adopts your daughter. The father will have to give his consent.