The ending of Batman and Robin resolves on three points: Gotham is saved from the freeze, Mr. Freeze is offered help rather than only punishment, and the heroes become a united trio. The plan to freeze Gotham fails and Ivy is overpowered. Freeze is jailed in Arkham Asylum, and Batman gives him a chance at help for his wife's condition. Robin and Batman repair their partnership, and Batgirl becomes a full member of the team.
What does that mean in story terms? The film treats Freeze as a villain with a motive, not only a threat. Victor Fries steals diamonds to power the suit that keeps him alive, and his wife Nora Fries (Vendela Kirsebom) is the reason he cannot stop. That is why Batman offers help instead of leaving him to the cell. In my opinion, it is the most generous beat in the film, because it gives the villain's goal of saving his wife a place in the resolution. Ivy gets no such grace: she is simply locked up, which perhaps explains why Schwarzenegger's villain gets the emotional close.
Compare that with Batman Forever, made by the same director. There, Two-Face and the Riddler are driven by a grudge, one scarred in an attack and the other rejected by Bruce when he pitches a brain-wave device, and Dick Grayson becomes Robin because Two-Face takes his family. Here, the villains are less tied to Bruce personally, and the personal stakes sit inside the team instead.
The Batman and Robin rift is the other thread. It begins when Robin falls under Ivy's spell, and Alfred's illness adds to Bruce's worries at the same time. Barbara, Alfred's niece, discovers the Batcave and becomes Batgirl just as the partnership could use another pair of hands. By the last scene the quarrel is mended, and it could be argued that the closing image of three heroes together is as much a merchandising shape as a story one, given that the studio wanted the film to be more toy friendly than its predecessor. That is a reading, not a documented intention.
The result did not hold. The film cost more than Batman Forever and earned less, and the series then reset with Batman Begins in 2005, directed by Christopher Nolan. Begins goes the opposite way: a single hero, a young Bruce falling into a well, parents shot outside an opera house, and Alfred raising him. After a team ending with a trio, that lone origin story reads as a deliberate answer.