This was a pretty good start. I like the environment, some of the cyberpunk situations, and I think it lends itself well to close contact with your daughter.
One downside was how rushed the sexual tension with the daughter felt. You just kind of start a little too quickly with her saying the 'I'm a woman, I have needs, I want you' without stakes or a catalyst to develop that kind of change. Additionally, the 'I want this' didn't make MC react in a more shocked way as a result of there not being that buildup or explanation of why that was a casual idea. I get that it's a game and we shouldn't delay part of the point of the game, but I think it can be introduced a little differently. MC just goes right into "you're being naughty" "I have to fix that" without much "no, that's wrong. I might be lonely but I'd never mess you up" protest.
My two cents? The Narrator scene can establish that sexuality is desensitized more than what's already stated, that sexual services by clones are for the profit of the Corporation, and that Lucy has come to use that to get what she wants rather than simply viewing it as "my needs" as a result of learning lessons on the streets. This gives an opportunity to add a motivator (what does she want from MC apart from just "I want it"), gives flexibility to future event choices (Lucy offering lewd solutions), and provides more role to the environment (the sexuality shown in the back alley can be surprising because it's not Corporate sanctioned).
Edit: I'd also remove the choice of the alley or the tunnel. Have the player experience both, since they serve two different purposes to expanding on the setting. One expands on the reach of the Corporation, the use of Clones, and sexuality in society; while the other expands on the power of the Corporation, the sexuality and resourcefulness of Lucy, the desensitization of sexuality in society.