Want to know my sad headcanon that explains Hawkeye refering to a mother and sister?
Tommy and Hawkeye meet in the fifth grade so around when Hawkeye's mother died. Tommy's mother moved to Crabapple Cove to be near her family while raising her two children after the death of her husband.
The two bond over their lost parental figures.
Eventually Hawkeye starts to call Tommy's sister Sis and his mom Mom. Tommy calls Daniel Daddy Dan or something like that. The two are joking around at first, but the families grow close and they basically adopt each other.
So whenever Hawkeye asks his dad to send his love to Mom and Sis he means Tommy's family who are still in the Cove and who Daniel would see regularly (as far as he knows Tommy is in a big city being a writer).
After Tommy's death on his table, even though there's nothing he could have done, he feels too guilty to call them that anymore.