What happened to Sophie in her last encounter with Arthur Fleck?

I get why your wife would think so, but she's mistaken. From an interview with SlashFilm:

In the end, you can question how much of it is actually real. For you, are there any visual cues in the movie that distinguish fantasy from reality?

Well, even the things that are there I’ll never talk about. We wanted to make the interpretation of the real versus what’s not real, a part of the viewer’s experience. For instance, his relationship to Sophie is a fantasy to him. Some people have asked me, “Was she killed?” Todd [the director] makes it clear she wasn’t killed. Arthur is killing people who’ve wronged him in a certain way, and Sophie never wronged him. In terms of what we did visually to play with the real and not real, there are callbacks and scenes that mirror each other. We leave hints using imagery or way we covered scenes similarly between scene. Outside of that, I like that people can have the conversation and come to their own conclusions.

_{"'Joker’ Cinematographer Lawrence Sher on Contrasts and Chaos", Jack Giroux for SlashFilm, October 23rd, 2019}

The other answer here is good already and answers the question but I've found another source that has some more insight into the scene which is helpful here. The interview reiterates the quote from Sher in Jenayah's answer and then has the following from Todd Phillips himself (emphasis mine):

IndieWire recently asked Phillips about Sophie’s fate during a video interview with Anne Thompson, to which the director doubled down on the answer that Sophie is alive at the end of “Joker.”

“He doesn’t kill her, definitively,” Phillips said. “As the filmmaker and the writer I am saying he doesn’t kill her. We like the idea that it’s almost like a litmus test for the audience to say, ‘how crazy is he?’ Most people that I’ve spoken to think he didn’t kill her because they understand the idea that he only kills people that did him wrong. She had nothing to do with it. Most people understood that, even as a villain, he was living by a certain code. Of course he didn’t kill this woman down the hall.”

The apartment scene is the last time Zazie Beetz is seen in “Joker,” but Phillips revealed there was an additional beat planned for the film that would have not left Sophie’s fate up for debate. The director said the script included a cutaway moment during Arthur’s interview with Murray Franklin (Robert De Niro) that showed Sophie watching the discussion on television. The shot would have confirmed outright that Arthur did not kill Sophie. Phillips cut the moment because he only wanted the movie to be told from Arthur’s point of view, and cutting to Sophie would have disrupted the film’s narrative structure.

_{Indie Wire, Todd Phillips Cut Zazie Beetz ‘Joker’ Scene That Confirmed Her Fate — Exclusive Video}

That deleted scene actually appears in the leaked script, as it's leaked though take it with a pinch of salt for whether or not it is correct.

INT. SOPHIE'S APARTMENT, LIVING 116 ROOM - CONTINUOUS

Sophie's sitting on her couch watching this interview play out on TV. GiGi's asleep next to her. The open envelope and the money are lying on the coffee table. No sign of the flowers anywhere.

MURRAY FRANKLIN (ON TV) Let me get this straight, you think killing those young men is funny?

JOKER (ON TV) Yeah. But comedy is subjective, isn't that what they say? Besides, the way I see it, what happened was a good thing. All of you, Gotham, the system that knows so much, you decide, you decide what's right and wrong. What's real or what's made up. The same way you decide what's funny or not.

Sophie edges forward on the couch, can almost see a hint of agreement on her face.

[...]

INT. SOPHIE'S APARTMENT, LIVING 120 ROOM - CONTINUOUS

Sophie screams and jumps to her feet horrified! Waking up GiGi who starts to cry when she sees what's on television--

_{Joker - Leaked script}

No matter what the director, actors, writers or productors says after the movie is released.

The complete scene is designed to leave the spectator in albis doubting about the fate of Sophie and her daughter. This is completely intentional, as it raises the tension of the spectator, creating a breakpoint where the main character can turn from society's victim to villain.

Now... if the script, or the director's vision had a definite answer on the result of that question, it would be answered in a later scene, showing Sophie alive or showing their corpse, obituary, funeral, etc...

But (and this is a great but): there is no answer on the movie, so the answer is open to every spectator. You have the option to determine what happened based upon your sensations on the movie.

If there was an objective answer, on the following interviews, creators could have said: she's alive (or death) because on x scene you can see proof of it. If there's no proof it's open to your thoughts.

Then why answer on interviews that she's alive? Easy, because after the movie is released there is a clear interest in selling the character not like the psychopath he's going to turn on but more like a society's victim, so at a marketing level, is better to say that Sophie is alive. But if this was the intention from the beginning, a simple shot of her looking at the tv when he's being interviewed would have suffice to avoid the ambiguity.

TL;DR; They made an ambiguous scene purposedly to increase the tension on the movie, and so there's no actual answer to if she's alive or not.