Ove didn't like cats in general because he felt them untrustworthy, but he and Ernest had learned to get along because Ove knew that Sonja loved Ernest unconditionally. Ove learned to fish with Sonja's father and fixed her father's roof and truck. Three years later, Sonja's father died. Sonja stayed in bed for three days and then began madly cleaning the house. Ove wandered around the farm fixing it up and three days later, they got a call from the grocery store that Ernest had been hit by a car.
Sonja's birth family disappears in a matter of days, leaving her with only Ove. Notice that after her father's death, she takes her time to grieve and then moves right on to frantic cleaning—exactly the opposite of what Ove did in the present after Sonja's death.
Nobody believed it was an accident: everyone who had met Ernest knew that was impossible. Ove and Sonja drove Ernest to the vet, where he died. Sonja leaned against Ove in the waiting room and told him that he had to love her twice as much now that Ernest and her father were gone. Ove told her he would, which was the last lie he'd ever tell her: he knew he couldn't love her any more than he already did.
Once again we see that Ove has a lot in common with these figures he doesn't really like. His suicide attempts in the present mirror Ernest's in the past. Ove also shows that he's willing to compromise his principles and lie to Sonja to make her feel better and cared for.
Ove and Sonja buried Ernest by the lake and then drove back to the town. Sonja had arranged to meet someone there and Ove never asked who it was or why. When Sonja returned from her meeting and got in the Saab, she told Ove that they needed to buy a house. When Ove asked why, she put his hand on her belly and told him that their child needed to grow up in a house. Ove was quiet for a while and then said that they needed to get a Saab station wagon as well.
Ove's suggestion to get a station wagon shows that he is very interested in following what they "should" do now that they're expecting a baby. Ove's principles likely keep him from asking questions about whoever Sonja is meeting. At this point, Ove is actively working on building community and family as they prepare to be parents and to move.