Betty and Hal

The father-daughter relationship between Hal and Betty Cooper is uncertain. It had recently suffered since the reveal of Polly Cooper's pregnancy by Jason Blossom, son of a family Hal despised.

History
Presumably, Hal and Betty had a good relationship before elder sister Polly began dating Jason Blossom.

During her childhood, Hal and Betty would fix cars together.

Season 1
The morning after Jason's body was found washed up on the shores of Sweetwater River, Alice and Hal informed Betty that due to the scandal surrounding his death, they'd be having a lot of late nights at the local newspaper they ran together, The Register. No one cared about an accidental drowning, but the murder of the sociopathic son of the wealthiest family in town was bound to make headlines.

Days later, Hal and Alice knocked on the door of the Andrews house. Hal first apologized to Fred Andrews for coming unannounced, but it had been a rough couple months for them. Before Hal could finish his sentence, Alice cut him off, she insisted that Archie Andrews and Betty stop spending time together. She claimed the relationship was toxic, on both sides, and their recent behaviour reflected that.

While Alice was off at a women and journalism spa retreat, Hal took the opportunity to work on his car, but was halted as Betty entered the garage, wanting to talk about Polly. Hal explained that Polly and Jason had a fight, he was unsure what the fight was about, but Polly was devastated afterwards. He came home from work one day and heard the water running in the bathroom, so he knocked on the door, asking Polly if she was okay, but she didn't reply. Hal then kicked the door down to find a suicidal Polly attempting to commit suicide, he claimed this was why she was sent away. Later that night, Betty spied on Hal as he watched old home movies of Polly, while drinking his sorrows away.

Hal later attended Jason Blossom's Memorial, where he had a run-in with Cliff Blossom, they had a brief heated exchange of words, seen by Betty, and went their separate ways. Once home, after Betty had been told by Rose Blossom, Betty confronted her father him with news that Polly had been engaged to Jason, however, Hal was already aware of the engagement. Betty wondered if that was what he and Cliff had been arguing about. Hal denied it and explained that their argument was about their families, and the fact that the Blossom clan came extremely close to destroying his family. Cheryl's great-grandfather murdered his grandfather over money. They had been business partners in selling and trading maple, but one day, Cheryl's great-grandfather decided that he no longer wanted to share the profits, so he murdered Hal's grandfather. The Blossoms stole their livelihood, and Hal would die before he'd allow them to steal his daughter too. Jason made her sick, so she would not be returning home until she was no longer sick. He warned Betty to stay out of it.

As she discussed the matter at school with Jughead, Betty had come to the conclusion that Hal was the culprit that broke into Sheriff Keller's house while everyone was at the drive-in on closing night and stole the evidence regarding Jason Blossom's death. Jughead then questioned how far exactly Hal would go to protect Polly, before adding the Coopers name to their murder board.

Having learned that Betty and Jughead secretly visited Polly at the Sisters of Quiet Mercy, and discovered her pregnancy, he questioned if Betty had found what she was looking for while she was there. Much to her disappointment, she didn't. However, that didn't stop Hal from being the target of Betty's suspicions. He hated the Blossom family for stealing the Cooper family legacy, as well as Polly being pregnant with Jason's child, which gave Hal motive. She accused her father of not only breaking into Sheriff Keller's house, and stealing the files on Jason's murder, but possibly being the murderer. Alice laughed hysterically at the notion that Hal could be Jason Blossom's killer. She claimed he didn't have the stomach for it, though she wished he had done it, or that she had done it, as Jason deserved it after what he did to Polly. Hal and Alice accused Betty of sounding just as crazy as Polly, who Hal claimed was distressed and delusional, and her story about running off with Jason, just a fantasy. However, Betty didn't believe them. Alice then told Betty that she may not believe them when they said Polly was crazy, but she would obey them.

Hal was a part of a search party to find Polly, which had been organized by Betty and Jughead, encompassing the eastern part of Eversgreen Forest, the most likely direction Polly would have gone if she was attempting to leave Riverdale unnoticed. During their search, the Coopers had a heated argument with the Blossom family, who were leading a search of their own. Penelope Blossom accused the Coopers of hiding Polly, a potential suspect in Jason's murder. Since the search was ultimately unsuccessful and to get ahead of the suspicions, Alice was forced to come forward. She held a press conference and dismissed all the negative rumours and announced that Polly was pregnant with Jason's child.

At breakfast the next morning, Betty questioned if Polly could return home since everyone was now aware of her pregnancy, to which Hal and Alice said yes. Betty then asked where the baby would sleep and Alice claimed that Polly had decided to give the child up for adoption. Hal firmly stated that that was her only option, unaware that Betty had secretly found Polly the night before, hidden in the attic, and knew her sister wanted to keep her child. Unable to live at home, Betty arranged for Polly to stay with Veronica Lodge and her mother.

After Alice kicked Hal out of the Cooper house for secretly making Polly and appointment to receive an abortion before she had been sent away, they reunited when Alice arrived at The Riverdale Register with Betty where they presented him with a USB flash drive that contained a tell-all exposé of the corruption surrounding the Blossom family. With motive and the capacity to see it through, Alice and Betty decided it was time for the Blossoms to answer for all the harm they had caused, everything up to and including them taking Polly, who was currently residing at Thornhill. However, Hal refused to publish Alice's article as it would only serve her personal vendetta against the family. Having been bitter after getting kicked out of the house, Hal changed the login password for the Registers' computer, in preparation that the day would come when Alice would require it's service. He explained that he was kicking her out of the Register just as she kicked him out of their home and that she was fired. Alice and Betty left, but Alice was so consumed with anger, she shouted that she wanted her daughter back, and threw a large rock through the shop's door, shattering the glass, much to Hal and Betty's shock.